Randomness and differentiability in higher dimensions
Logic
2015-09-29 v4
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.
Cite
@article{arxiv.1410.8578,
title = {Randomness and differentiability in higher dimensions},
author = {Alex Galicki and Daniel Turetsky},
journal= {arXiv preprint arXiv:1410.8578},
year = {2015}
}
Comments
19 pages