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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

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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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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