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1. Oct 3, 2014

### jamilmalik

Hello everyone,

I was wondering if I could get a simple introduction to this Theorem since I will have to be giving a presentation on it within the next month. Based on the statement itself, there is an assumption made in the hypothesis which is something I haven't quite understood yet:

If $U$ is an open subset of $\mathbb{R^n}$ and $f:U \to \mathbb{R^m}$ is Lipschitz continuous, then $f$ is differentiable almost everywhere in $U$; that is, the points in $U$ at which $f$ is not differentiable form a set of Lebesgue measure zero.

What exactly is Lipschitz continuous? I asked a professor of mine and he said to think about it as a bounded slope which makes sense looking at the definition of Lipschitz continuity. However, could someone please provide a thorough explanation of this? For instance, how would one go about proving this Theorem?

2. Oct 9, 2014