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Math Help - Two Lipshitz functions...

  1. #1
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    Two Lipshitz functions...

    Can anyone prove that the product of two Lipschitz functions is itself Lipschitz? ( Lipschitz : a function f such that for all x,y in D, there exists an L > 0 s.t. d( f(x), f(y) ) <= L*d( x,y ) )
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  2. #2
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    Quote Originally Posted by Kurt14 View Post
    Can anyone prove that the product of two Lipschitz functions is itself Lipschitz? ( Lipschitz : a function f such that for all x,y in D, there exists an L > 0 s.t. d( f(x), f(y) ) <= L*d( x,y ) )
    This is not true: take \vert \cdot \vert :\mathbb{R} \rightarrow \mathbb{R} (absolute value) is Lipschitz but x^2 is not. If D is bounded however use \vert f(x)g(x) - f(y)g(y) \vert \leq \vert f(x) \vert \vert g(x)-g(y) \vert + \vert g(y) \vert \vert f(x)-f(y) \vert
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