Suppose that E is a measurable set of finite measure and that (fn) is a sequence of measurable functions, which converges pointwise to f on E. Show that there exist closed sets {E: k e N} so that (fn)...

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Suppose that E is a measurable set of finite measure and that (fn) is a sequence of measurable functions,<br>which converges pointwise to f on E. Show that there exist closed sets {E: k e N} so that (fn)<br>converges uniformly on each set Er and so that<br>00<br>m E<br>0.<br>%3D<br>k=1<br>

Extracted text: Suppose that E is a measurable set of finite measure and that (fn) is a sequence of measurable functions, which converges pointwise to f on E. Show that there exist closed sets {E: k e N} so that (fn) converges uniformly on each set Er and so that 00 m E 0. %3D k=1

Jun 04, 2022

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Suppose that E is a measurable set of finite measure and that (fn) is a sequence of measurable functions, which converges pointwise to f on E. Show that there exist closed sets {E: k e N} so that (fn)...

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