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I am struggling with the concept of "locally Lipschitz". I have read the formal definition but i cannot see how that differs from saying something like: "A function is locally Lipschitz in x on domain D if the function doesn't blow up anywhere on D"? It seems that, when talking about local Lipschitz, you can always pick the domain small enough or L large enough to satisfy the condition; unless it blows up.

Maybe an example, that I am struggling with, may help. Is |x| locally Lipschitz, and why?

I, by looking at the derivative which is sgn(x) am convinced that this satisfies the Lipschitz condition, the way I interpret it, but still, i would not bet my life on it. :)

Thanks

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# Locally Lipschitz

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