Real Analysis : Cauchy Criterion for Uniform Convergence
Prove that A sequence of functions (f_n) defined on a set A subset or equal to R converges uniformly on A if and only if for every e>0(epsilon) there exists an N belong to N such that Absolute value of f_n (x)-f_m (x)<e for all m,n>=N and all x belong to A.
© BrainMass Inc. brainmass.com March 21, 2019, 10:56 am ad1c9bdddfhttps://brainmass.com/math/real-analysis/real-analysis-cauchy-criterion-uniform-convergence-30034
Solution Preview
Please see the attached file for the complete solution.
Thanks for using BrainMass.
(Cauchy criterion for uniform convergence).prove that A sequence of functions (f_n) defined on converges uniformly on A if and only if for every there exists an N belong to N such that for all m,n>=N and all .
Definition (Uniform Convergence). The sequence converges uniformly to f(x) on the set A if for every , ...
Solution Summary
The Cauchy criterion for uniform convergence is investigated. The solution is detailed and well presented.