Suppose the sequence (fn) converges uniformly to f on the set A, and suppose that each fn

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Suppose the sequence (fn) converges uniformly to f on the set A, and suppose that each fn is bounded on A. (That is, for each n there is a constant Mn such that | fn(x)| < Mn for all x ∈ A.) Show that the function f is bounded on A.

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Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

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Question Posted: Apr 07, 2016 11:07 AM

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Suppose the sequence (fn) converges uniformly to f on the set A, and suppose that each fn

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Given 1 there exists K 0 such that if n K ...View the full answer

Introduction to Real Analysis

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