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surable functions such that g_n→g a.e. on a measurable set A of finite measure, then given eta>0 there is a subset B is subset of A with m(B)

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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Question

If (g_n) is a sequence of measurable functions such that g_n→g a.e. on a measurable set A of finite measure, then given eta>0 there is a subset B is subset of A with m(B)<eta such that ,{g_n} converges to funiformly on A~ B.

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