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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


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    try a direct proof.
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