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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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