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Rademacher's Theorem(that every Lipschitz function on $\mathbb{R}^{n}$ is almost everywhere differentiable) is a remarkable result on the structure of the space of Lipschitz functions, but I was wondering whether it has any interesting applications. All of the "useful" results(or maybe "applicable") that I know of about weak versions of differentiability involve estimates(eg Sobolev embedding, Lebesgue differentiation theorem.)