# Norm and Uniform Convergence

• October 11th 2009, 07:44 PM
6DOM
Norm and Uniform Convergence
http://img237.imageshack.us/img237/1420/62874853.png
Any hints on how to approach these two questions?

Thanks a lot
• October 12th 2009, 02:09 AM
Enrique2
For a) just observe that A is compact.

b) is immediate from the very definition. Uniform convergence to f certainly is equivalent to the convergence to 0 of

$\{\sup\|f_k(x)-f(x)\|: x\in A\}$