Let (fn) be a sequence that converges to ƒ uniformly on a set A CR. Assume that |fn(x)| < M for all x € A. Show that if g is continuous function on [-M, M], then the sequence (go fn) converges uniformly on A.
Let (fn) be a sequence that converges to ƒ uniformly on a set A CR. Assume that |fn(x)| < M for all x € A. Show that if g is continuous function on [-M, M], then the sequence (go fn) converges uniformly on A.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
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