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Exercise.) Prove that if f is a real function on a measurable space X such that { | f(x) 2 r} is measurable for every rational r, then f is measurable.

Exercise.) Prove that if f is a real function on a measurable space X such that { | f(x) 2 r} is measurable for every rational r, then f is measurable.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.5: Permutations And Inverses
Problem 5E: Let f:AA, where A is nonempty. Prove that f a has right inverse if and only if f(f1(T))=T for every...
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3, Exercise.) Prove that if f is a real function on a measurable space X such that {a| f(2) 2r} is measurable for every rational r, then f is measurable.
Transcribed Image Text:3, Exercise.) Prove that if f is a real function on a measurable space X such that {a| f(2) 2r} is measurable for every rational r, then f is measurable.
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