Lipschitz function and uniform continuity

atm06001 · Sep 25, 2008

A function f:D[tex]\rightarrow[/tex]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[tex]\rightarrow[/tex]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?

mathwonk · Sep 25, 2008

try a direct proof.

Lipschitz function and uniform continuity

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Lipschitz function and uniform continuity

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