please help me to solve allni need it please Question 4(1) Prove that a sequence (fn)n converges to f in measure if and only if forevery k N, lim m ({\fn - f\ > }) = 0.n→∞0(2) Prove that if lim m ({\fn - ƒ| >0}) = 0, then (fn)n converges to finn→∞measure.(3) Prove that if a sequence (fn)n converges to f in measure, then the limit fis unique, almost everywhere.(Hint: first show that for every e > 0,

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Answered: (1) Prove that a sequence (fn)n…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.1: Infinite Sequences And Summation Notation

Problem 73E

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(1) Prove that a sequence (fn)n converges to f in measure if and only if for every k N, lim m ({\fn - f\ > }) = 0. n→∞