Question 3. Prove the following miscellaneous facts:(1) Prove that a function is simple if and only if its range {f(x): x E X} is a finite set.(2) Prove that every positive bounded measurable function f : X → [0, ) is a pointwise limitof a decreasing chain of simple functions.

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Answered: (1) Prove that a function is simple if…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Problem 1RQ

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(1) Prove that a function is simple if and only if its range {f(x) :x € X} is a finite set.