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Thread: example of absolutely continuity

  1. #1
    Dec 2010

    Wink example of absolutely continuity

    I'm studying Real analysis,

    It's known Lipschitz continuity implies absolutely continuity.

    and Cantor function is an example for uniformly continuous function but not a absolutely continuous function,

    i wonder if in between case, if f(x) is a holder continuous which is uniformly continuous but not lipschistz continuous, what's the result?

    In any reference, the example of absolutely continuous function was Lipshitz but is it true for holder continuous function?
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  2. #2
    Senior Member
    Dec 2010
    Something that is holder but not lipschistz:

    f(x) = sqrt(x) around x = 0
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