Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Lipschitz function and uniform continuity

  1. Sep 25, 2008 #1
    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?
    Last edited: Sep 25, 2008
  2. jcsd
  3. Sep 25, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    try a direct proof.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook