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4. Let EC Rd be a measurable set such that |E| > 0, and assume that ƒ : E → [-∞, ∞] is a measurable function on E which is finite a.e. i. Show that there exists a measurable set AC E such that |A| > 0 and f is bounded on A.

4. Let EC Rd be a measurable set such that |E| > 0, and assume that ƒ : E → [-∞, ∞] is a measurable function on E which is finite a.e. i. Show that there exists a measurable set AC E such that |A| > 0 and f is bounded on A.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 23E: Let a and b be constant integers with a0, and let the mapping f:ZZ be defined by f(x)=ax+b. Prove...
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4. Let E C Rª be a measurable set such that |E| > 0, and assume that ƒ : E → [−∞, ∞] is a measurable function on E which is finite a.e. i. Show that there exists a measurable set ACE such that |A| > 0 and f is bounded on A.
Transcribed Image Text:4. Let E C Rª be a measurable set such that |E| > 0, and assume that ƒ : E → [−∞, ∞] is a measurable function on E which is finite a.e. i. Show that there exists a measurable set ACE such that |A| > 0 and f is bounded on A.
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