Let (X, E, µ) be a finite measure space. We write An → A as n → ∞ if and only if1 An (x) → 1д(x) as n → ∞ for every x € X. If {An}%=1 C Σ and An → A as n → ∞, thenshow that μ(An) → μ(A) as n →∞.

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Answered: Let (X, E, μ) be a finite measure…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter9: Systems Of Linear Equations

Section9.7: Puzzle Problems

Problem 10OE

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Let (X, E, μ) be a finite measure space. We write An →A as n → if and only if 1 An (x) → 1A (x) as n → ∞ for every x € X. If {An}a_1 C Σ and An → A as n → ∞, then show that (An) → (A) as n →∞.