kindly answer letter b. 2. Let ([0, 1], L, m) be a Lebesgue measure space, and let A be a nonempty measurablesubset of [0, 1]. Let {E}[0, 1] be a countable disjoint collection of Lebesguemeasurable sets.a.Show thatm (AnŮ Ex) = m(k=1k=1Σm(An Ek).b.Let f [0, 1] (0, 1] be a measurable function. Show that for every € > 0,there is a natural number N and a set C such that m(Ce) < € and< f(x) ≤ / / /for all x € Ce.11NE+1

We have given that f be a measurable function

Answered: b. there is a natural number for all x…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 10E: For each of the following parts, give an example of a mapping from E to E that satisfies the given...

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b. there is a natural number for all x € Ce. Let f [0, 1] (0, 1] be a measurable function. Show that for every € > 0, : N, and a set Ce such that m(Ce) < € and 1 Ne +1 < f(x) ≤ № c