Please solve 5 Let S be a closed n-cube with v(S) > 0. Suppose (fk)kEN is a sequence of functions#5from S to R, each bounded and integrable on S. Suppose in addition that (fr)kɛN Convergesuniformly on S to f : S → R. Prove that f is bounded and integrable on S.

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 25E: 25. Let, where and are non empty, and let and be subsets of . Prove that. Prove that. Prove...

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Let S be a closed n-cube with v(S) > 0. Suppose (fk)keN is a sequence of functions from S to R, each bounded and integrable on S. Suppose in addition that (fk)kɛN Converges uniformly on S to ƒ : S → R. Prove that f is bounded and integrable on S.