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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-'({-0}) e M, f({0}) E M, and ƒ is measurable on Y.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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Section: Chapter Questions
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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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