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Is the following statement true. Assume that $f:[0,1]\to [0,1]$ is a continuous function such that $$\sup_t\limsup_{s\to t}\frac{|f(s)-f(t)|}{|t-s|}<\infty,$$ then $f$ is Lipchitz continuous.

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    This "smells" like it's related to the [Dini derivatives](https://en.wikipedia.org/wiki/Dini_derivative) of $f$.2012-10-14

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