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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 50E
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In Exercises 1-7, (X,M) is a measurable space.
1. Let f : X → R and Y = f-1(R). Then f is measurable iff f-({-}) E M,
f({0}) E M, and f is measurable on Y.
Transcribed Image Text:In Exercises 1-7, (X,M) is a measurable space. 1. Let f : X → R and Y = f-1(R). Then f is measurable iff f-({-}) E M, f({0}) E M, and f is measurable on Y.
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