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Consider a sequence of non-negative measurable functions {f} defined on ECR that converges pointwise to f: E → R. If fn ≤ f almost everywhere on E for each n, then show that √p³n = St. fn f. lim 7→∞0

Consider a sequence of non-negative measurable functions {f} defined on ECR that converges pointwise to f: E → R. If fn ≤ f almost everywhere on E for each n, then show that √p³n = St. fn f. lim 7→∞0

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 27E: 27. Let , where and are nonempty. Prove that has the property that for every subset of if and...
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Consider a sequence of non-negative measurable functions {f} defined on ECR that converges pointwise to f: E → R. If fn ≤ f almost everywhere on E for each n, then show that √p³n = St. fn f. lim 7→∞0
Transcribed Image Text:Consider a sequence of non-negative measurable functions {f} defined on ECR that converges pointwise to f: E → R. If fn ≤ f almost everywhere on E for each n, then show that √p³n = St. fn f. lim 7→∞0
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