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arXiv · 1410.8578

Randomness and differentiability in higher dimensions

Alex Galicki·Daniel Turetsky
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Abstract

We present two theorems concerned with algorithmic randomness and differentiability of functions of several variables. Firstly, we prove an effective form of the Rademacher's Theorem: we show that computable randomness implies differentiability of computable Lipschitz functions of several variables. Secondly, we show that weak 2-randomness is equivalent to differentiability of computable a.e. differentiable functions of several variables.

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Alex Galicki, Daniel Turetsky. 2015-09-26. Randomness and differentiability in higher dimensions. https://arxiv.org/abs/1410.8578

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