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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: ke N} so that (fn) converges uniformly on each set Er and so that 00 m E 0. k=1

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: ke N} so that (fn) converges uniformly on each set Er and so that 00 m E 0. k=1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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) converges uniformly on each set Er and so that 00 m E 0. %3D k=1
Transcribed Image 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
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