# On differentiability relative to a n-rectifiable subset of \mathbb{R^N}

Let S be a n-rectifiable subset of \mathbb{R}^N , we define the differentiability of a funtion f:S \to \mathbb{R} at a point x_0 in S as in Federer's book, where he called differentiable relative to S at x_0. Are there any known condition to ensure that f is differentiable relative to S at H^n-a.e. points in S?

Here we suppose that S is equipped with a metric d such that it is Ahlfors n-regular in Hausdorff measure, meaning that the Hausdorff n-measure of balls with radius r in S is comparable to r^n. That is, We may view S itself as an n-regular n-rectifiable metric measure space.

-