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I t that there are functions continuous everywhere but differentiable nowhere.Then let c(t) be one of them. And let μ[t1,t2]=c(t2)-c(t1). So in this case c(t) is not differentiable.

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If you take a more advanced course in measure theory you will learn that monotone functions are automatically differentiable almost everywhere with respect to the Lebesgue measure. This of course covers cumulative distributions.

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Thanks for your advise. –  Yangzhe Lau Mar 16 '13 at 14:46
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