Sequences and Uniform Convergence
Let {fn} infinity-->n-1 be a sequence of continuous real-valued functions that converges uniformly on the closed bounded interval [a, b]. For each nЄ I let
Fn(x) = ∫ x--> a fn(t)dt a<x<b
Show that {fn} infinity-->n-1 converges uniformly on [a,b]. (Hint: Use 9.2F)
Theorem 9.2F;
Let be a sequence of real-valued functions on a set E. Then is uniformly convergent on E ( to some function) if and only if given there exists such that
---
https://brainmass.com/math/real-analysis/sequences-uniform-convergence-58107
Solution Preview
Please see the attached file for the complete solution.
Thanks for using BrainMass.
Problem:
Let be a sequence of continuous real-valued functions that converges uniformly on the closed bounded interval [a, b]. For each let
Show that converges ...
Solution Summary
Sequences and Uniform Convergence are investigated. The solution is detailed and well presented.