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1. Let f : X → R and Y = f-1(R). Then f is measurable iff ƒ-1({-∞}) E M, f-'({∞}) e M, and f is measurable on Y.

1. Let f : X → R and Y = f-1(R). Then f is measurable iff ƒ-1({-∞}) E M, f-'({∞}) e M, and f is measurable on Y.

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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In Exercises 1-7, (X,M) is a measurable space. R and Y = f-1(R). Then f is measurable iff f-1({-∞}) E M, 1. Let f : X f-'({0}) E M, and f is measurable on Y.
Transcribed Image Text:In Exercises 1-7, (X,M) is a measurable space. R and Y = f-1(R). Then f is measurable iff f-1({-∞}) E M, 1. Let f : X f-'({0}) E M, and f is measurable on Y.
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