3-25 Listed Main properties of the
definite integral that we will prove:
Included: Monotonicity. Linearity. Additivity. Bounded
Constraint. Continuity of Integral Function for integrable
functions. Continuous Functions are integrable.
Fundamental Theorem (Derivative form) for Continuous
Functions. FTofC (Evaluation form) for Continuous
Functions. Mean Value Theorem for Integrals for Continuous
Functions.
3-26. Additivity. Continuity of Integral Function for
Integrable Functions. Continuous Functions are Integrable.
Excerpt from Spivak, Calculus, Ch 13
Theorem [Additivity]
Proof: [Converse proof omitted]
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zDwDaG1DywVG375KKnBD+uc+fIVxyfIJDBGUFfBU+1+veD7Ck6vw10ji3PoMeOz/2PN+feVue27BnVH51jS9W5YQrkJX5MPSWyOEVq0bKnqMzlrs6xJalvsAPsLdd4ybarKcJEZTYGNohtb1R/dI4tVeeGaSipVir/CPWbJXuKzhu/c2xJ6hssw8b4xwXcrqACc5XZGNggNlHV69wnF/WPf1zkhgHHup7+wUUAbnEQ0FfBo6v4GVk/RatHfufYkgxfw05O/N/2pj9ego1q0p8rS8/Y9kb1R+fYUnVumAJ5iR9Qz8N6oyCL+nJlT9F59TvHluSwLVljb7nGS7ZdTRHulmVXVB/D2x1X38CyNW+YhpLKpf6PUL9Zsqdou/fbBpZq0GAPyn1j/OMCbldQgbnKbAxsEJuo6nXuk4vaxj+ubatQU92qw/HVAK5wCtBXwXOr+AFZP0Wf533bwFIN38EOz/2vjemP679dQQUmyrIrqo/h7Y6rb2DZmjdMgbzct5d0vLh97C1IwRR5adZPUb9qjwss1XAnHZ77tL3lGi/ZdjVFuFuWXVF9DG93XH0Dy9a8YRpKKpf6P0LxZqmfok/vtQ0s1aDBHpT7xvjHBdyuoAJzldkY2CA2UdXr3CcXNYx/XNUOEVa6Xo23VQb4jSOAvrIfWvVPx4Knb9uHfdvAUtX3WEMb0x/Xf7uCCkyUZVdUH8PbHVffwLI1b5gCeblvLOl4WRvaWJaCKfJyrJ+ieMmeGFiq4TY6PPdpe8s1XrLtaopwtyy7ovoY3u64+gaWrXnDNJRULvV/hOLNUj9Fn95rG1iqQYM9KPeN8Y8LuF1BBebKsiuwcXiiqte5Ty5qGP/HDbg9wkrXq/G2ygC/cQTQV/ZDq/jRWPP0bfuwbxtYquEL2OG5/7Ux/XH9tyuowERZdkX1MbzdcfUNLFvzhimQl/vGko6XtaGNZckePzXHghruXbInBpanvsHOcEzFxg3w0e7w/1f/UAXWTfOGaSipXOrfX/1mKWiGtnu/bWB56hssyQEpfB30ZvjVvrV6BtYwpGzN++SihimMC9shwjLXS/G2ygADjgD6yn5oFT8aa56+bR/2bQPLM3z7Ojnx/9hYgfESbFdQgYmabInqSoS74+obWLbmDVMgL/eNJR0va0Mby5I9fl6CNTXcu2RPDCzPcA+dnPgiFeumfye3ja1nVNn6N0xDSRWzBP0Vb5aaZmi7/XtGlWrQYM/K/YAUDtO8tRoG1jCkAs375KK2KYzL2yfOPNcr8JKCABc5Begr+7lV/HSsefq2fd73jCqVN7A/zqjAeDU/2h3+/+ofZ9vYekaVrX/DFMhLf2NVxyvbTU1NfitL9vh5OdaUcfuq3Qpsd1C5muyjx1Gxbvp3cs/YekZVoH/DNJRUMUvQX/FmqWmGntu/Z1TZBg32rNwPSOEwzVurYWANQyrQvE8uap7CuMjdog10Mc3j6wBMcBDQV/YjvPJFoewB3PPVp2dU2QYNdnzu/6YCrfRvy56x9YyqQP+GKZCX/t6qjhc3yo8z3oqhrCC/xZM9fl6aNWXssHBPiSpVn330OIrWTf9m7hlbz6gK9G+YhpIqZgn6K94sNZ3Qc/v3jCrVoLsel/gZWRyjf2s1jK1hSNn698lFj0hhXO22YU87Ozsgm8OC1lIfb5WvCGUP6Z6vBT2jSjXorrMT/04RWunfmT1j6xlVgf4NUyAv/WOqKpGV8ZPKVbYcZRkdEFWqQXednfg6RWvlEZ3cM7yeUWV7RMM0lFQxq9Bf5X4p64SeJ0DPqFINuutxiZ+RxTH6t1bD2LrFU6B/n1z0rBTGZe8f/xXnZQQUc17QWuoTruwhWvmQ7vlm0DOqVL+lfHzi3ylCH49oy57h9Ywq2yMapkBeBY4p7BlZ/JGaS+WGKluRsowOiCrVoLvOTnydorXyiE7uGV7DkAo8omEaSqpYt1UYt0cfTWqSPVf4+L9NtKWwF6PaG1K2Pn2+7owsjlHfWndH7tYw3eKpccYR9NwUxvV/ShbfHZMIsJEjg76yH3Jlz9HK53TPl4OGIWX7bSHekPt/KEIfj2jLnuE1DKnAIxqmQF4FTirsGVl8+QcAy3M16YGGIWX7bSGOT3ydurUy6OSkRZkYuWHPNAypRn3DHCCvYq1WYdwb3WwvS/ZE4eMP5qqv6iNCKtChw6Mck8gZBq2VsSgTI3drmG7x1DjjCHp6FsPN+rx0vpq93AIP5dSgr+znXM17QPGjuuHLTcOQCvyW9fGJf6cOfQzaMmlFJkZu2DANQ6pR3zA95VXgpMIemUV4LmW7qXI5ypJ6dEjZfkv5+MRDqFsrxc08N3LDnmkYUg1H34S8orVaiEGaDW0vS/ZE4eMP5tpS2Ish7YqnQJMOD3FGFscobq25wbs1f6tgahT3SZ4zsvg65X+O9dCwgW6cGvSV/ZyreZQWP6cbvtl0i6fAYBXOTvw7RWiluDPnRm64d7rFU6bhWmyRV4STantkFuG51Gyo4qaqSerpIWX7LeXjE1+naK0Ud/L04A23W7d4ahQ3zDHyitZqIcbt0c32smTPEjv+lRmLC9s8ngJNOjzEGVkco7i1pgdv1TatgqlR3Cd5Dkjh38br0j/BB4UKdObgoK/sR13Bs3/Lo7rbC023eAoMWuvsxL9ThD6K23Jl8G5t0y2eGsUN01ZqBU6q7ZFZhOdSs6GK1+K3pDa2Qbd4CgxW4ezE1ylaK8WdvDJ4t87pFk+N4oY5Rl7FWi3EuD262V6W1FliB78yY31hm8dToEmHhzgji2NUttbK4K3apk8kZSr7JNUBKfxovEBt04wNsnOmQCp7nr6yn8cFT/0tLxPdXmW6xVNg0FpnJ/6dIvRR3JYrg3drm27x1ChumLZSK3BSbY/MIjyXgj21paOyk3p6PAUKWutU6tbKoJPDF2Vx8G6d0yqYMpUNc5K8inVbiHGH9NGkJnlTRI18a9L62n6MZ1cwNZp0eIhjEjnDoLViF2Vx5FZt0yeSMjVNUuCMLH4z3M0d8w2MbXGQnvUBLrJp6Sv7MZz9sN/1DtHtDaZVMDWyW+tB1KGPQVuGr8ji4N3aplUwZSobprPUCpxU2yOzCM+lYE9tWYjspELi2RVMgUFfnZ14CHVrpayZ10fu1jmtgilT0y3nySuateivYNdsaYBuR0GrYAoM+uqJiZ+RxRnGrRW4Lusj9+n/mkha7Y6aJilwQApXjNerVeJRUS2O0LM4wHV2LH0VPGPynvQbn45JGcXGkzR+4LDTBk3VJMJKitBHWWeuj9xt+xQE0yHN/6jplv5Si3BSeY/MIjyX7G21q51Sk4qKJ2n8wGGnDfqqSYSdKVof404OXJeQkVvtuJpgtqf5HzXdcp7UilmL/rJ3zcYG6NN+NefS9jR/C6bJKqw4I4szjFsral2iRm7SOQU7sUmm43g6BHbXASncMl64DhUICWZxhIZlAe6yXemr4AGT9Izf/lzs82zOflHok+k4pCax1VOEJsZtmbolAwOOCnI9kthg+iQ7DqlJbMWK98tzy3tkFhm55O2sjb2UlFHPYPpkOoinSWyPoGh91DRz4Mh9mqdg+/dJdhxSk9g6S62YtXiEvI2zd/X7tF/BudQn2d+C6RDYnDOyOEZqd4WP3KRzssNIWo6MeDZGNeeAFOZ8XMRddViPZDGLbgUB5tiu9FXzgAl/nnV4KPZ5Nqe+KMQuXHZIewPbQhH6qOnMwJH7dE52G2cvSnhUewOrV7/6UYMXOzKLjFySNtf2RurTzOG1vTL4rmTHIe0N7BEUrZXUZs4YuU/zZEeStChJIe0NrL/UilmLR0jaO9uXvs9pkB1GxvIlxbMxqmkHpHCMj601tzoZY45HnhttWnYMGaXLi2dLSNOeHv+ij0tZX5DFGNaD71MKYIXtSl9lD5ioR1qfJ2Kfx3NqGFELF2gc0q6odlGBPlI7M2PkPjsoO4y8dUkKaVdUW2RX4JjynpHFl38AsKBPM6dGEr52qfHsXYhHUK4+kpo5dYP02XHZYSQVMC+kXVE9Qmq5rMVThG+fJuvepAOzwwhfvrxg9vbDnKfHf4yLrXVlmQKHmgt7erSeMSSVLiOYXVHNeXTwsVqt6XQAITE3KQKwyHalr8oHzMrTvefjsEk8qWFML1mSj120vSuKvTz9PpI6M7vbm/RPdhh5BUwKaVdUW2xZ/cDxy5yRxZd/ALBgPZfUSFIH35LsOJIOC/EIatXE3X4eLFPgUNORrwzYM4y8AmbEszGw/rJrZSEeJGr7tFr0JsFkhxG1dqlhdFiIOc+N/DB3GyxWbNiBZZkLIDaGpNLFhrF3FeY8NOw8fRb0bhiBAfcpArDCdqWv4gfM+ME2IS/U6XQOC6NP/Z/VG2Vem3grd5tzsEyBQ01HvjJgzzDyCpgRz8bAttiy+oHjlzkjiy//AGBNk3hSw5heskAfO2d7hA+iRE2sdPW68MijyrISQ2wYeQWMjWT7WvS3pVUCxyfWyg5qu++2x1NQlulVqwlge3grnhjzeVYaLEps/FGVmZs9PIDU6oUEsDG2FY8LuEyHyqx03WK0D+1n4N9sV/qqf8AsPlO7PQi3R5VdnA6r8PQmyfPClHtaadF14cGH1GQlgPAwsmsYGMnetdgiO+tjCntGFl/+AUBCOh1iCAyjwxLM98fuDulGiTpY6eco4SmEVGYlgPAYsmsYEsPe8J4iuz7q/zgrO6vncm+PqiCA7avw6A4Ze1zA51nprkDhKUTVp8PsqdULCWBjbNOeFe0W24uzq+Ue18zAd3Ysfe16xsw9Vhs+BbeHlx1Ah7U4o1UyvC3fhlaaM0pGCiHF6RNAdg1DYtgb3i67Vj92ihpnZPHlHwAs2x5VdmWarMKjm6QP9dluupNjZWQRUp8+AWTXMCSGveE9wq5WiZ2CcCubq+da7w1s10YrzvfpTfKbxwV8nunWihWeRUhx5qbOmD21eusB7I1tzrOifbMtzaY34OlsWvra/gpy/cna9hHYsIAFUxQne7dPOj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EOP
Theorem: Suppose `f ` is integrable on `[a,b]` and there
exist m and M so that for all `x in [a,b]` `m \le f(x) \le
M`. Then `m(b-a) \le \int_a^b f \le M(b-a).
Proof: Consider any partition `P` of `[a,b]`, then
`m(b-a) \le L(f,P)` and `U(f,P) \le M(b-a)`.
Now since `f` is integrable,
`m(b-a) \le L(f,P) \le lub {L(f,P)} =
\int_a^b f = glb{U(f,P)} \le U(f,P) \le M(b-a)`. EOP
Excerpted from Spivak, Calculus, Chapter 13:
Theorem: If `f ` is integrable on `[a,b]` and
`F(x) = \int_a^x f ` for `x in [a,b] then `f` is
continuous on `[a,b]`.
Proof: Since `f` is
bounded on the interval `[a,b]`, we have a number `M >0`
so that for all `x in [a,b]`, `-M \le f(x) \le M`.
Now consider `F` on the interval `[c,
c+h]`, of length `h>0`.
Then `F(c+h) = \int_a^{c+h} f
` and using additivity we have `F(c+h)
- F(c) = \int_c^{c+h} f `.
By the previous result we have
`-Mh \le \int_c^{c+h}f
\le Mh` or
(1) `-Mh
\le F(c+h) - F(c) \le Mh`
Now consider `F` on the interval `[c+h, c]`, where
`h`<0, and length `-h>0`.
3-28.
FTof Calc I and II, MVT for Integrals. Alternative proof
of FTofC using MVT for Integrals.
Excerpted from Spivak, Calculus, Chapter 14:
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lvsdrRy9p/pfk9Hb9NjtrZqqYya/1aZ+bFNw7zY6T5/Ce0ExBucLLT8YXjgpl1A5EC+cO9XxWZuSSQ5CglvZS03zS9zXs0Oczym6e8YHmSQLbJ19/YeL7H+WpVkf4sNXNJsrVYzj3BAhVW112Kne90/MqSgqs+jvTjWqup5lc8Nsm4bF5iNlu7yK+1mqqu+2VV85l8fXJWHZ3Ovzi5XG3C+ct/LfVxoZkim800GMscG1dy0UzL8y/OZ8inTY50dYnVxlcrzGeYrDl+fflye5p6nHBrmbEEZnvOjhQuHagTWL1qdDN1MvVrjcOMQ5b3EiiSX33cxUzLk9XmI83HC3eUTFViKWdAVZ75F+f7DQwnc8lqwsWJfi47+frwEvmEqzMJXzhfYbKp+bJLV8UWimXmcPYVAAAA+EvHw6COZ2RXZUsC36Lkkd/Th/AyVRt6zraGg2WaGo/l/+tcVT5nnjONhO1vJ6a1x3yp2gkH6oQDLHX9sX7tHO4yOY2lIskw4csHNffs0epatcF2dpqMNJ9t/sX3Np5sc7JaSZh/lfq4UGFfkwnDTcWChS9fXXoy+VXB+WYnI3Xknw9ZEuljtsl1z0wSG+n4qqr51PZSEjJ87e3DmY+0GrJw1OEM8wUDl8yvXnhhoOWJ2c/WD1zSLdxLrObV/9ua56pyrJFMhlXjaVyN9OPlgYWSgTME0MePAAAgAElEQVRtDl4THto4VeCScF+vlOw3PLGlTZ958c6dqlo6XKR85snY+7dgxjjnTOa+iWVaWFp6UCfWXclA8nWSXbSKpZrpKNZa4PLAopOxr2pOdjqzRCDhx4Gslp18ZfkSSxXC7Y+rjQsWxvhYdun1TQvxUDYVAAAA+EvHk6Dww7VA2ZLA+wWG0zFSCsW25uRtTabK9zUYzrjmCfOcD/9nwkDLh2vqZXWwq0XyYTJdZNaNNVUyhxuFGx9U6M68ZNsG3X7zbOu0KtjHbKuN3Nt4uM35aoWRVut3tzZfKtnIx2rJRqpa+LXa5IrzeQL5lwIvSRYsjHRCkvycxxXCw8noC5MseMh8ZiKtxpupkyxV0l34wnD4TNpA13P78LYjduUF55dIDnmmYKaXWIaM8Eg3jz187cy6+S7mIyXnUF7nQe6d2+TuX5W9cb+a5rYhQNXEbhz+vKuQS5nDF46LJLuYv3xcJ1a5YyCxvvK9lOsbb9WoM41U5f+12vyK4cnErlpteX718BKB2OW9P3QXfg0QXqUkOQeyqQAAAMBfOp4EDZ6sZZZ4zaOr2GQ6RpoMfJruOayOKHzh7e1cBSspslQntu8nzHMm+Thb4JKTdTQSG2xHtnsDfJzDfLX8KG4UnsBTut6TM7BKYOaxDCdsSizYagu3d104/9Y6scol3VWNKN/OVZF8jHz+qzozL1sNUxh+5tqlmiVFVuuckOTq8tUw4zqBvvI6kpywZeUK925DqWRryQBNV1VdPq5zb6Qq+Y4mCy7VLxn1ValkL6sBSsRGupo/M/PMrCbXzbTQFGlDkQcpbLZp+z4WvGu/8uveVaFqYpMbdK+rkKtpOy5PdjF/+cdSt6Ta01SsYEbreAOl7tqjj/l/LbW0YmwysauW+l1aOrZELHZH74/bhavVwwtVhec0dhQAAAD4S8czoKsHZMlV3vHcKjyWjpFmAp+pdRRLI8pce1cj41SFpfLz+Vjn9nl+TD4TLHPtaTq6KJxPskLH5UtFxqPY2ctdPk4g4O6e/m1DztgS5TM8eVPyIwoslE69rHD+e26M1bL5VHv6ClcoyZAMPy7y8WXJJJnwM9fOFywsNV/tkCRX1wbCDEqFW8soT3LIlpUr3LgNpZIV8hlWL+lecb7OvZGqlDQ1U3C18iHTPmS/wlNdSp6ZeXJQVXOOTakpUkmMpyhvNlltfCdcVbtrv/Lr5mPHMlRNbH6PbnQVsmS/5ivcuPRMqRMGEu5oUDBZszZJIEx+s/IxapeeKTK/VngymZF+rLm0bmyJ2gpVjT9lF35dOrxQVXIOZEcBAACAv3Q8A7p6OpZc5QXPrZIzKR9pZtEztY5iaT57Lu9QHqljPjNF7h3mOPlksOTlR+noonA4mTr5DPlGBhVWp1Eyz/3GE4i5u6d/6w4ZnkP5DE/elECwWAv3dl04/z03xmrNZIXCpgYFJ2uWhAkHGO5J6ve0QDslowtMr6PaVcEHJbmKUT7hTGthe1qrjReullG4a7U3QLJOUzt9gbuL3JinUFVfHwsGynZUWLq8JEOJzFTnY4d3LXxhYYVxnapSJWFWkzxCeafJ6Q3uhHGdWzYrOb2S4ccGXrJ0ePXNrkJum/bVhSWrrxYZdLEzUlWA7pqFMcJJkgXzMQqXnq+w+rLVeJmRhjOXrJgs0tr4I3bhat3wQoXhOY3tBAAAAH5+2v7+dPWAKbnK0x9a5QdyywTGu3ma7mlMDmdnhXLleTI9nrPXSwaxv2QCf+roonA4N+7R4PL5RrpHsVpkv/EYA+5u6N+6cybr18Y7eV8CwfJTrQi+pnD+Z94YmSKFw8nXLAmTGWzm2vmygasCqySTdw8huSmbk1xdctdMytUmMahMqcJqG64dFxnUub3rcPINkarUtjYouH/sJ2SoUjjVwCqxC/cs3VTnqtRdYQ7X1Gmm5lWkmSL7d6qj03yApVmFly7solt4SvOlAhdWNVJVJ7xrVQMJBxjXzJctyZCMEa5ZkqR29dpNydSvzTZzeclaycwdO/L0XQiseFUkOUlOYzsBAACAnx8HlvbqeH7XFHWw4uE2DOTjZPYXKdSUJ1zzkL1eNYi9mv+hE/hTRxeFNcOlZvZ6UCdzbUn++WqxUntM7sKSu3v6t9ac+eLl2Y7dl0CwcCM3dl04/8J9rL0r8vuSzzCuOVP26sJfrx28eE+AeeFqS68vTN4xhKuyj0hyFSOZpKm7e5McsmVNjh1UuFRJjKsi4zo3dj0T/sZIVWpbGxTcPPaSDIW9JO1JEl6ib9TbWpgsdVeYwzW1mRng1bVnzj+Tc6nTwYtj46qacGz1zQpDZkrl53NCFyWpagN0ly3JkIwRq1mSJNNR0zRmlui+dlBtftHkQrFSHTvyrF24WvHXqwYv7pgkp7GdAAAAwM+PA0sbPfqh2+qTxLscMpN8nabMN+YJz+qQ7V41iL0a/qET+FNHF7U1Y6U+7nXeU0Zxo8AMS8a+U2vOkuK1wY7dmkCqMxsZK8xc2HvtJGOlmnYzXPbqwiqZAOUDWbowvEosefkEwgkPSXL1+mSYjpq3Jzlky5p0DyrcUbjUVYxfLx+8ONbOCQMsKdJULalqRB0FM6Wurv318sGLy+cTsydJeIl8sKruCkeUj7Rhyw7R1GZmgFfXnjn/TM5BpyX6ks90ESjVpzZkptQho67dskC12h3pLluSIRkjVnMpzODF4Y6apjGzRObyTIzyF19dG87csSPP2oWrtFUCyTmW7QQAAAB+fhxY2sVDt/cp2dAD74qmPOFODxzRR1eZa2+Sw4fwp44uamvGSn3c7ry+8HuqbZAc4COazdwed1XuSHVssI6rblSY9sxS4WpNWxkue3Vhidbkt5TtW6UpbSDhCUmuXpxP0lT23iQnbFmf7kGFOwqXuopRJdZOJnlJndpU4WpJ5ZtSWzBc6ipGlVg7YXtihFfJZ6tqsHBK+Uh7du12fW1mKl9de+b8MzkHnea1Jp/pIlCqT23Iu/ot7KK2hUC1phnWbnRhgHyGWNlBnhJNsZckl6hK2NHaeKFw4I5NedYuXC1XYjUzh7OjAAAAwM+PA0u7eOj2MlW392k3Rl+ecOXTRjRjcHsU3iSHD+FPHV3U1gyU+rjXeX3ht1Xr1jHA1sAxyQZXy94+hMcFi111Qke/Ksx5ZqlwtaYdjN0bV1fFqu1Mfm/l8iXOGcIhSa5enE/S1+BdSQ7Zsj6FMWo7Cpe6ilEi1ksydkmp2mDhaknl+1JbMFxqsPt5sV4y9iQJr5LPVtVg4ZTykVqbmrS6VkDf0pm+bhxIQDjq/J3Q1H7VKiWBV6exulDtVAtLJRcNL13bwmq12u1IhqlVu00zlcN58vpiL0kuUZKwo6/xQpnAHZvyoF0YzLB8LLyAOwAAAAD4+XFgaQsP6d6nakNPuzH68oTfBaeNaMag2cKb5PAh/Kmji8KasVK1e51RG+D2dpaU7ML5zTbdZifcvUvBbs8WSzVo55C+/qUw4ZmlYtVa964wT1WkGX0BBt21zjxQ/JYhnJxkNXY+RrLsjUkO2bI+hRlq24mVGkz19lGHA5fUrE0YrpZUvo+1BWOlhpt/0PDn7UkeXiWfrarBwinlI5U0dVVk3mLfy1rXDRe/axox4ag37vsgQFWdpVKDUUzaELKjVGa5ji5qQ66+vmqGO3dncvWSDIGygzDbprRhrfwShRXW46cS3tVvR81tu1AyQ76H2wIAAAD4+XFgaQuP7V6makMPvDFaI8WKHzilj64yF94k5w/hTx1dFNaMlTpnd2oznNDRvMEuzMc+v9OOO+2cG/hB2cKpBh2d093/K8x2ZqlYtdZdOy3PpL4MV5ULV6kq27oRS8UPSXL1ynyS1gZvSXLIlvUpDFDbTqzUVYbNU50xiJpMXtv+UcMs39zCguFS1zt/3E07aU87tQPfs3R5ksJIJU1dFZm32Pea7nXDxW+ZRlg46u1tVq2eb+SqwrwNITtKxRbq66I26urrS2a4bXdWA+QzBMr2hWmNfcsSyQp9Ux1sYjJt7aY8aBc62ufF3BkAAADAz48DS/065sC9qjb0tBuj+16NFT9tSh8Nxlh4k5w8gSsdjdTWDJQ6Z4NqM5zQ0aTBFizFfm6np9Wskt/TzcEy1x7V4H8VBjuzVKxa35bFKvflmdea4ap41VolBTuCxUJ+Q5LWBvcnOWfL+hQGqG0nVuqEkY5d31OXSpaoDRyullS+v4UFw6XKm7rdno5qB75n6fIkhZFKmroqMm+x7zXd64aL3zKNsHDU29usWj3fyFWFeRtCfqwWKzUfNdN+dwur1Wq3Y0/lZIB8hkDZ26exJ0PJEpkiO5sayBfvCLytyPyLO9rnxdwZAAAAwM+PA0v9OubAjQo39LQbo/tejRU/bUof1Y6xe1N26miktmag1DkbVJvhhI4mDbZgKfPhbf5s/A7lIUM4Nl4m1fBufUCbbyoVq9a3WYHKV5eU5JnXnWHQZn65kmrdGzFf/JAkrTFaG9yf5JAta1UYoLadWKkTRnrl+m76z8f/N79QbeZYtbzyPLUFY6VOG3Leno7Cq+SzVTVYOKV8pJKmrorMW+x7Tfe64eK3TCOstsedbVatnm9kMI1JG0J+rBYrNRPyP9W/F9W2EEhV2Mi2ypnV72rt3mlsy1CyRKZIbUdXSf5T9znQsSlP2YWSAfJV3BkAAADAz48DS/08uXuZqt088K7ovldjxQ8c1FjhGAelTp7AlY5GamsGSp2zQd1z2N/RpMEWLGU+vM0fB5aOiVd4s83oayQQ8vWlPlbr26ZA5atLSvLM684waDO/aEmd7o2YL35IktYYrQ3uT3LIlrUqDFDbTqBU936FTaaqCt+9CzfOszxPbcFAqasANw45b09HmVWS8aq6K5xSfuYlu3ZVZN5i32u61w0Xv2UaYbU97myzavV8I4NpTNoQ8mO1WKmleIVddE9jXK12O/ZUzqx+S2utYfpi37hErMj+Lc7327EpT9mFq5zJ9nkxdwYAAADw8+PAUjOP7d6nZEPPvDG6U8WKHziogdoZnnmfhHX0UlszUOqcPeqew/6OJg224NjMMeU9Hj63Y+OVpBrftyf0W5jkQaU+Vuvbo0Dlq0tK8szbk2HQbGbpkvDdGzFf/JAkrTFaG9yf5JAta1UYoLadQKnu/QpYClMV/tg9zSvPU1swUOoqwI1DztvTUWaVTLzC7gqnlE9V1ddVnRmraxVma63fd+Etanvc2WbV6iWNDAby0baQ42obShV20d3CuFrtduypnFn9ltZaw/TFvnGJWJ2Sjkp2NrlcRwsH7sJV/WT7vJg7AwAAAPj5cWCpmcd2L1O1oWfeGN2pYsUPHNRA7QzPvE/COnqprRkodc4edc9hf0czBvM/M3BGbZvnz+3YhIWpxjfwvS0XxnhQqY/V+jYoUPnqkpI887ZlGPQbXr0kfPdGzBc/JMkgRj5Ja4P7kxyyZa0KA9S2EyjVvV+rVpNUhT92T/PK89QWDJS6CnDjkPP2dJRcpfDCnTfMUqmlant27V5XPVa1GS7+rOHX9rizzarVb29kRm3I1tHt6aJ7Gtsa2VY5s3pJhtWyfUlaY9+7xGqdknbCi4b77diUp+zCVc5k+7yYOwMAAAD4+XFgqZnHdi9TtZtn3hjdqWLFDxzUQOEMz7xJMjraqa0ZKHXONnXPYX9HMwbzPzNwRm2b58/t2ITbNuLelrt7PLPUx2p9GxSofHVJSZ55mzMMug4EKAnfvRHzxQ9JMoiRT9La4P4kh2xZq8IMte0ESnXv15JYhpLw3btwyzyb8tQWDJS6CnDjkPP2dJRfJXDt7TdMX7A9u3av7h7D9Z81/Noed7ZZtfrtjcyoDVlSKlahddcCda5KjavVbseeypnVSzKslu1L0hr73iXCQy4MH86ZWTS/KU/ZhaviyfZ5MXcGAAAA8PPjwFIzj+1epmQ3m94ded2RYvUPHNRAYdozb5KMjnY2DDx21f5tKsxwSEczBvM/M3BGbZvnz+3YhB2pxnfyLV1332xnlvpYrW93ApWvLinJM29/hkHjqwFKwndPYL7+IUmuXlYSprvHzUkO2bJWhRlq2wmUugqweaS/JglfGAjfvQv759mXp7ZgoNRVgBuHnLeno/wqq5eX91VYrWka5bt2u9YewzN81vBre9zZZtXqtzcyozBkSanw5a1dBOpclRpXK9yObZUzq5dkWC3bl6Q19r1LLJXK9xLOnOy3Y1OesgtXxZPt82LuDAAAAODnx4GlZq95bDfe0HPcNYRb6nRoTRXr+sxB/apwZ0++ScI6OiqsGSt1zk4VZjiko48Gwz8zcFJtm+fP7dh4fcGOup+7b7YzS32s1rc7p+WZd1eAq96XYlQNsHUISyEPSXK9Jw4sTdU5LWR5hsJStdViAW4fafjCWPhj9zSvPE9hwVipq6tuHHLennZK5jZfoWObCgvm43U0eKDWNsOVnzX857ZZtfrtjcwoDJkvFb62u4tAnViqwkZmKufLJgOUxFgt25ckH3vDEuFV5quVL1SesK9Cd83WXehonxdzZwAAAAA/Pw4sNesYwn7j3TzN/jmUFOkOn4zXV7zpqlsUTu/YOySjo6nbZ3511f7NKsxwSEcfDYZ/YNq82k7PH92x8bqDHbI13TfbmaU+VuvbmljZvjzz7g1wNYHNA2zdiKXKhyS53hMHlrrqzBcvqXxLhtpZxUq17teMzNJV4Y/d07zyPIUFw6VOG3LennZK5nZVZEZTC4Wllqr1tXmUzbs5WflZk69tc2enVavf3siMwpDJUpkM3V0E6sRSFTYyUzlfNhmgJMZRc563IUBtm5PVylcpT9haobtm6y50tM+LuTMAAACAnx8Hlpp1DGG/8W6eZv8cSop0h0/Gu7HymYP6VdX0Tr5DMjqaKqwZK3XOZhVmOKSjjwbDPzBtXm2zh4/u5Hgbgp3Qe2GAB5X6WK1va2Jl+/LMuz3AVYadG9q3EauVD0ly9eJ8kr4G70pyyJb1KcxQ21Gs1L1TTS5dFf7YPc0rD1PYYLjUaUPO29NOydyuinzU10JhqaVqfW0epW9DM5WfNfzaNnd2WrX6I/arcNqZUskM3V0E6oRTFQbIhyl0FSCfIVD29mlcZdiwRGaVmYKZVZJp8/12bMqDdqE8Ku/mzgAAAAD+0vEs6epZVcfDtarMHTqGsN94N0+zfw5Vk+xLPq8vW7jysbP6l6qdPfwOyehoqnBW4VKHbFlhgBPamTGY/IFpSxQ2e/joTo63J9jtvRcGeFCpmWpNWxPLc3VVSaRJ964+jhEb4LbVOyofkuTqxfkkfQ2WJKmqs3/L+hRmqO0oVurGqebXrQp/7J7mlYcpbDBc6rQh5+1pJz+3qwoDG1ooLJWfRizM4Zo6zZR91vDDaa/u0m3NVi39iP0qHHW4VD5AdxeBOuFUhb1sKJsPcEtrt0/jKsOGJTKrfCyYWSIfNd9vx6Y8aBeuKueHwCu5LQAAAIC/dDxIGjyrCq/yxIdf73hmN97N0+yfQ9UY+5IvacoWLnvyrP6pamcPvz0yOvoqHFe4VNXWJxUGOKGdjwZjPy1qocJ+D5/eyfECwWLh7+29cPgPKjVTLXzhs/LMu3f1ZJLC8E1zuLepTNlfX58P01S2KsntpTaUvTFG7dbHSl1l2DDb/KJVyY/d07zyMIUNhktdXXjjnJP29JIc2gljL1w938ub7sCxpk7L78Z8pCblnW5rtmrpR+xX4ajDpfIBursI1AmnKuxlQ9mSDMkYgbJNSfKxNyyRWWU8t+QS+aj5fjs25QW7kB8Cr+S2AAAAAP7S8SBp8BQsvMoTH351DKE24fy6j3DLEKoG2Bp+XlO22tHl85Qr2dbD742kjtYKJ5YpdcLGFQY4oZ2PrkIeGLVQYb+HT+9l2WL5722/+067N1UmWG1Hh+cJJ0+u/rPrXVMYvnsOtzSVKfvr6/NhmspWJbm91IayN8ao3fpwqdoYmbSri1YlP3ZP88rzFBbMlDptzkl7eikceHm2SYWDyt9CL7sJBzo67Rh+Jk+rTNqm22ymSOHSTV3Uur3fkgDdXQTqZFIVZsiHKXSVIRkjVvb2gWxYffO0M/VLSuWL7JxYR818/Y60P3M/fHkcOwoAAAD8pfBB0q81D3/41apwCI/o990yWzl+R/xa567t7nijZQqWh2mSn1vH5I+y7daK1cyUuro2091qhcLVO3aq3GDmp0UtVNhv+fRqx37yzgayhfPf2H73nXZvqmSwwhh9eTKRbp/GaoZBmNXXh/OX78JVzRckCYcZFEw2WBjm3lLjmpmCJySpHVS4VMd+/X/Z1kWrknfvQn6YYeV5CgtmSjXN+a7N2nPPhIfWHWxe4aDyt1DTTXim8k47hp/J0+fAO22yQuG65S10uL3fkgDdXQTqZFIVttNaszBG+ZA/1mwayHyRDdvR0eN44OH6JaXyRXZOrKNmSf2+guEKnMmOAgAAAH8pfPJ1VbNkiY5HdRuUzOFB/b5YeCvHb4c/i9y+3eVvtEzB8jAdZrY1VqE2Xkm1fIzuWytW86gdrAqQX71qp2pdJTwwarmqfgun1zH2k3c2kC3cwr3t57eg8DarivQxW/e1j8iTXz28dCzDIM/Si5P5y0dRe0vsT3I13toJlzRYGKawWnm8TMETkpwz89okPxOfePkVryoEYnfvQmaSSX07my+YLNXXWrhCfunWeyY8se5g8woHlb9/yu/Ak5V3mqz2oMkfeKdNVihct7yFDrf3mw9wVaGwi0CdQbC+C1cLZmoekmRQ8GPNvjmHk4eXnl8iv0pm5n1RSyJ1TOxBu9AUuKplTmNHAQAAgL/UPvn6s2DVs6qmR3Xd8nN4Vr8vFtvKj2+HfxU5Ya8zt+tkwRvDdPi4rbHLm4LlyxaGKb+1wjWTpa4uz4fJBAgsfVUquVO1BtM+KmeHDRu9VLBj8ofvbCBeuIt7J1B4b1TtZnepyWq1TQ0KztcsjFSydGDdQdnwhR+vrd3K8lHU3g/nJInlGZTKNxhQG+OcLSvXPaVYtWSp2t3/mfjgbQr8a5GPlQt7L59kXtPO5gsmS5WP+sbN2nPPxCa2Idik2h0vqbZn4w7ROvwbw3Tru9NiLc9fW7joVbVYqSYdQ14qlQxwdfmvRcJ5JsNMZuu+drJUprWMwjDj1j4WLJ/JUoUN29G06ZmZN0VdijSuXD6xB+1CR+aqSBzIpgIAAAB/K3w49TPx5DewSusDtVbJ5A/q9PVWt/LPF4wrHLXXhZGSdc6cz79k9rG1wdOmVx6msMF8qasKq3kKV19ad1wquVO1BqM+KmeHwq7zM2ya/OE7G4h31HjnFd4bVb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Theorem: If `f ` is continuous on
`[a,b]` then `f` is integrable on `[a,b]`.
Proof [From Spivak,
Calculus, Ch 14]
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WOFRW7cpaJSjW23ploqRWtmcf5QWMz39WH9kwy2pWacHgygd3YKLuEmeCxWVWepqQpiAqbukLWuypnrKLw5pzU6g83nQ+0u0oAAACATzYsCknaYIrdqBqIlrpZVmobLqPSwIBR6Q3HubqwyPT9VLD5k4nV7/lfjUtlfQNjo6XWGC4jvew5Tepe48R1jV589ucdWeBwUeHrZ4GoJGMrnYmWWtGa6ZsfNzb5ja24T+BGSPy8zHsvGR4opIplsquYCR6bVeWZSpqCqLCpK2S9q3LGKgpvzkmt/nDT+UC7qwQAAAD4ZMOihNQNptiNqoFoqZtlpbbhMioNDBiV3kycq2uLzOCHgs2fTOyJDb8XOFBszpOXF5ygjNzqTMTMECETtyD/vY4scKao8CWULSrDwDInU0qtaM3czY8bm3y1Vvwb/f6/zo+Sl3/vJcMDhVSxTHYVM8EDsyo+UxnpBc5s8e51CWxLeLSbmMPRSrlpV6DdVQIAAAB8smGx05oNptiNqoFoeZtleZHr5BMYMCq9mThX15aax/tsA0PFRhvOoWyr/+UWnnl2qPZoN6VFZRglI6s6EzEW/H9x6zM1/wqOLHCmqJtlU7NLUbkFFjiZUkhFe2ctL//AfLJb0ThoSG551Q2kN5bM1UBRhayRXcVM8MCsis9URnpRMYu3rtdVOWMVLZu4mYB13DQ/0O4qAQAAAD7ZsNjjfgspdoMpcKNqLKu8zbK8yHXy2T59GXGuIpSazas8A0PFRhvOoWCTf6ZUoYEz+Y8FKTVZGflUm4jhsPOjJ+Vfx5HV5c17wXZFZRVY2mRKIRVtn6/JoWMzX9yKrrHypnu6jsH0xpK5GihvmjJkVzETPDCr4jOVkV5IzKsgdVrXK7acZRM3E7COm+UUaHeVAAAAAJ9sWKzWuHMUuMEUuFE1llXeZlle5Dr5bJ++pDhXQepPaGCo2GjDOezqcFcmFRqYmtjN7FSer8lkCk7EWG7zo5ea63CnVhdS11WQah2LSimwrsmUsqevv6AR2zuQGrB3rOzc8qobSG8smauBkqYpSXYVM8EDsyo+U+HpRU1rVJw6AstJas5J3f5w07FAu6sEAAAA+GTDYp2uDaPADabAjaqxrPI2y6ptw2Xks3368uLchCoypwWbP5NYqfb2plGhgbsSqzxlk5k8ayJSR68z0RlOrS6wrqtQdZoWlU9gUZMphVRUYaZiOxCbSVIrxoZImu6hCpoi3wcfS+ZqoIxpypNdwkz8wMSKz1R4elEBr+LUaV2X2FqSOnNMt3+6WU6BdlcJAAAA8MmGxSK9u0WBG0yBG1VjWeVtllXbhsvIZ/v05cW5j1ZhTgOTWdC04RzWt3csge0NbA8109Kbado4ZTeJhcfcnt5YkMnR60x0hlOri63rKlqRpkXls6Bjay6/D7J4pgZGz0h7TStiZ3xy6KjqBlo3lszVQOHTlC21hJkWBSZWfKbC0wsJeBWkVOu6BNaS15ljuv3T/YqKsrtKAAAAgE82LFYY2yeK2mAK3Kga2/bK2yyrtg2Xkc/26cuL0xJz77QGZhJb1FioIr0dHn17A9tDzbf0ZrK2zNpNSuEx96Y3HGFy9CKznOTU0jJm7Srm9tZFJRNY0WRKIRUVmabeBJJyXtCHgtPdX0RMemPJXA0UPlPZUquYiRyYVfGZik3vemE+8jc5UGA5eZ05qeEfblZUoN1VAgAAAHyyYZFueJMoaoMpcKNqbNsrb7Os2jZcRj7bpy8vTnvkXdNasPmTiW3v7fDQRRqYnVhj8MWzdp9MeMyN6Q1fPj96kVnOoLTAyBtbF5VMYEWTKaVWtH6a2nPISzi7DzPBQ6rOK3Ag8lgyV32InakF8qqYjByYVfGZik0vJNpVkFJ96xJYS2pbjmn4T/eLKsruKgEAAAA+2bDINbxDFLjBFLhRNZZV3mZZtW24jHy2T19enN7462e2YPMnE9vb2JlxizQwO7GuIZZN3E0adWLOtyj22vURylJaePwt3YvKJLCcyZSiMikyR9eL5bvUHIoED6k9qcCx3MaSuRorcKbWyKtiMnJgVsVnKja9kGhXQUr1rUtgLaltOabhP90vqii7qwQAAAD4ZMMi0cz2UOAGU+BG1VhWeZtl1fbgMirdPn15cfYOMZxGYKjYaOvT6DI5bpEGZie2d5SBHOrEnGzRZCbzE7R9fvPMN6esBaXV6V5UJoHlTKYUlUmRObpK46vsHIpEDik/qcCx3MaSuRoraqZWWjkdW7IqPlOx6c1Hu4pQqmm9osrJbstJPf9wv66i7K4SAAAA4JMNiyyT20OBG0yBG1VjWeVtllXbg8vIZ/v05cUZGCV2iJU5xDZtONRVGtm9nR+xSAOzE+sdKHyUxQkUmYj5NOaXwfb5zTPfnLLWlFake1HFBpYzmVJUJldprJymmxxW5pY30HzkkD4kFTiW23AyV8NFTdYyK6djS1bFpyk2vcloV5dXa1qvkFoW9OSknn/4urRC7K4SAAAA4JMNixTze0OBG0yBG1XDWSVtllXbhstIpsL0zccZG2v7zBZs/nxisZksSPgmwpYGhiQW1YSxnMdkrJztExGVxnxzwntbx9tKu68uaoHNJT5ifpHfxNmSUlRFsaECR1+WwH0mSWF7I9cJEhVzOJOrEScLWW/ZdCyOcB+qzjTFpjcT7eragk3rElXLgoYc0/OfWlbXvN1VAgAAAHyyYZFifm8ocIMpcKNqOKuk/bJq23DLagwMNRBtIM7YWNtntmDz5xOLzeQjbN6IdRoYklhUE8ZyHhM7BTcxF6cXUtd8kIz2FnFqXX/e9K/hrzmMZRK4HiZTiqooNtTPsF1DT444KaMJV2F7I9cJEhVzJpOMQrZYMx27Uio+TbHpzUS7uvYmznCqKycipMOBc7RslGUdbtGyuubtrhIAAADgkw2LeCF7Q4EbTIEbVcNZJe2XJYUtlU+F6ZuPEzVW7+WTCjY/JLHYZP58m9+Q4Uo1cD6x4UGjpmxA7BTcxFycXkhd80Ey2lvBqXX9NVDdcAe2NzBqKgPXw2RKsYszNtqftqWyfVXc5xOV1XxvryL0phc+y1cxszOJasivMYcjzAyaNx0bUwqfo1ix6V2uyM7vaL8GmUl18XTMd3hZwoEDrezwWD4Z9tYIAAAA8JMNi3ghe0OBG0yBG1UzWWXsl1XbhsvIp8j0TcYZHm7vzBZsfkhiscn8+XZwOD/cVYRdDWzJrf2qmeHGch4W2LeraIsnIiSNqwghQdoj1HRqXX8NVDfchO0NjJrKwPUwn1KpZK4Ctg86PFaU2A7ch22PfHX5r0HuI7fHyS5tPo28QsYiDEudjmr5bOnwlbwl1B7w5qpfg8zkOZbhjMmxHpTqfZy8tGdSirWxQAAAAIBf2bCIN783FLvBFLhRNZNVxpZZRsxS+cQGjIo2EGd4uL0zW7D5UaEy8kka6+ryX4O0RA6sfTja8LghOQ8L7NtVtMUTMZ/G1eW/BrmPHNveIo4s6p+BxTPch+09HCg2KUhgtMBkQvL5GapruNHEw8TO79ewXyPfXHgV4T7scCZd0bKvza5l4PJJIVVsn9PsaOHWFHsV8+cf3EeYTzI84Nhway4PyTYkSGrak1kF2lggAAAAwK9sWMSb3Bvq2mBqiRy4UTVTWviWWXuXVlpT495oA3HGRtw7rVdljmVSMFR4kN6Evw53c+FVhMmwjVW3ROu6amysgWwn9Rbb8l+zJ6J3LkIuvIow0JDG8ss6sqh/BlbOWCsqNHCg2PYgY0XNh+qN0Du/Y6U1XhvVxiixk9sY+Sr4/SVXEb4mPJDJQKiZy1fm8GucrgsDTVYx2YH7NIYDBobKEJveTeu+GggSnuFY1QPDDV8bnmH4iIs7HJJVlF3VAQAAAFyxYRFveHtoYIPpa9jYjarJaIHJdHVppdh8YmsMiTbW+bERN07rfZm9yTwr1NjlsTnfX3IVYT6Z9vKHS7u6cGC4rlRDtBf7Nc+VE9E7F/PJ/xrhazK9yX8trYLe6XiQgZXz61UDY8UV0Wqs2K4gvXVlp3TzlwMBx/IZTn4mhzGpo7dXd/NfOzo1+g3ZzYWNceZ70h7ha0UDl/eOHiuqiuFCbpo5EDYwVJLY3L52r2W4gUuiMhyLOTBcxlVJ2YYEWVbCWFZRdlUHAAAAcMWGRbyBHaKxPaaWXafYvar5UCHJtLdovd6Ubv5rbJkh0b4G6aqld6yueoe11NieUlSc9mghxfZeEpX2zX9tCXKTT9flV0GGoyW18f7vkyTVPtCQlfnc/2VvGgO13PxlS5d26e3AgwxP9EBDtjdwuNj2y/OihVQXErD3kvDMhysKTGPNKFcjzid59ZddNQ6M29WN9jhfo3Vd1Ttuhq5aFjQwpLHDobKFpzTfydSO5UXuHa7r72Oz6so2JMjiQnqzirKrOgAAAIArNizite8T3fzXkF2n4QsHos3HCUljrLRA7Sk1/qf5MtujTSYzEKQ955ZKJ41VepVbzVCBVXcNFBJ8OJ+Q0WOno2vEX/++pe1Jhgvv7lpnT4ajjYX6X9D6nMmkedL2eGLON3pn59d6e6dyVwNDih2Oc1VmYKjhsHnd6x0lZKCBQecTWDPQWJz2NL4G7xo6vAktAdsjf/2zruGydTVqspDYgdbkHCU8n/nCU3uVGnxsxPUpdaUaEmRxIV1ZBdpYIAAAAMCvbFikCNk/Gt5ymhx3MtpkfxZnkmEmz95r7ysNibYmyP1fTs9Jk7FKr9KrGSq29tT4Y3ECq4uNNlxIe2IrDZTceFVjsYGhxqKNxYnqbVfAjZ6Y842uqbmqt/3v93YvpNjhOFeVBoYaiLyrh+FDBOaQHX9grMk47dfOJDnQkLzIM/F7R1lpTRWxTQsMtUBSPpMlp3Zpy0S0NGRNJr1JRsXZUtHXlGJtLBAAAADgVzYsUkTtHA1cNTD0TALtoYZLu/mvgfnE6mhW2jdke0NdRRiIOTcV40Jym2naWJD23IYHGogcGDwjt0kDo/+8pLE/u2r81XCS91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3-29 Discussion of Improper
Integral for Discontinuities on bounded intervals.
This discussion defines the integral for a function with a
single point of discontinuity `c in [a,b]` by `\int_a^b f
= lim_{c*->c^-}\int_a^{c*}f +
lim_{c*->c^+}\int_{c*}^b f `.
Example: Find `\int_{-1}^1 1/{sqrt{|x|}}`. Work left
for reader... [done in class.]
Sets of Measure Zero introduced. [revised slightly from
class]
We say a set S of real
numbers has measure zero if and only
if given any positive number ε,
there is a family {In}
of closed intervals such that S
is contained in the union of the In
and the total length of the In
is less than ε.
Countable Sets have measure zero.
Suppose `S = {a_1,a_2,a_3, ... }` then `S` has measure
zero.
Proof: Given `epsilon >0`, consider the family of
intervals, `[a_1,a_1+1/3 epsilon],
[a_2,a_2+1/9epsilon], [a_3,a_3+1/27epsilon], ... `
then the sum of these lengths is
`epsilon(1/3+1/9+1/27+...) = 1/2 epsilon < epsilon.`
EOP.
Continuity, integrability, and measure zero sets related.
Consider the function `f` where `f(x) = 0` if `x` is an
irrational number and `f(x) =1/q` when `x = p/q` where the
gcd of `p` and `q` is `1`. Then `f` is discontinuous only
at the rational numbers and `\int_0^1 f` = 0. Discuss how
the discontinuity values are nullified by using the fact
that the rational numbers have measure zero.
The Cantor Set: has measure 0 but is uncountable.
Discussion: Consider the sequence of unions of closed
intervals:
`C_0=[0,1]; C_1 = [0,1/3] cup [2/3,1]; C_2=[0,1/9] cup
[2/9,1/3] cup [2/3, 7/9] cup [8/9,1];...`
The intersection of the family of these sets is called the
Cantor Set. It has measure zero and is one of the
"monsters" of the real numbers since it is not countably
infinite!
See
Cantor set - Wikipedia, the free encyclopedia