Randomness and differentiability in higher dimensions
arXiv:1410.8578
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.
19 pages