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…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Problem 1RQ

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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 →∞.