Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Randomness and differentiability in higher dimensions   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.

35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph