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Math Help - monotonic function

  1. #1
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    monotonic function

    Can you help me proof the theorem: i f f is a monotonic function defined on an interval I, then f is differentiable almost everywhere on I, i.e. the set of numbers x in I such that f is not differentiable in x has Lebesgue measure zero.
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  2. #2
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    Quote Originally Posted by haimap View Post
    Can you help me proof the theorem: i f f is a monotonic function defined on an interval I, then f is differentiable almost everywhere on I, i.e. the set of numbers x in I such that f is not differentiable in x has Lebesgue measure zero.
    This is a classic theorem of Lebesgue's. I believe there is a proof in Royden's Real Analysis.
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    Edit: Whoops, I misunderstood the OP's question. Please disregard.
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