# Lipschitz function and uniform continuity

1. Sep 25, 2008

### atm06001

A function f:D$$\rightarrow$$R is called a Lipschitz function if there is some
nonnegative number C such that

absolute value(f(u)-f(v)) is less than or equal to C*absolute value(u-v) for all points u and v in D.

Prove that if f:D$$\rightarrow$$R is a Lipschitz function, then it is uniformly continuous.

I am having trouble proving this, I am not sure if I should suppose not or go about it by some other method?

Last edited: Sep 25, 2008
2. Sep 25, 2008

### mathwonk

try a direct proof.