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Uniform Convergence in Metric Spaces by TOM DAVIS is a document available to read on EtoBox.

This document defines and discusses uniform convergence in metric spaces. It begins by defining uniform convergence as a sequence of functions {fn} converging to a function f if for every ε > 0 there is an N such that ρ(f(x), fn(x)) < ε for all x in the domain and n ≥ N. It then states that if fn is continuous for each n and f is the uniform limit of fn, then f is also continuous. Finally, it introduces the Weierstrass M-Test, which says that if |un(x)| ≤ Mn and the sum of Mn converges, then the sum of un c

Author

TOM DAVIS

Language

EN