Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the differentiability of Lipschitz functions with respect to measures
  in the Euclidean space   Rademacher theorem states that every Lipschitz function on the Euclidean
space is differentiable almost everywhere, where "almost everywhere" refers to
the Lebesgue measure. In this paper we prove a differentiability result of
similar type, where the Lebesgue measure is replaced by an arbitrary measure
$\mu$. In particular we show that the differentiability properties of Lipschitz
functions at $\mu$-almost every point are related to the decompositions of
$\mu$ in terms of rectifiable one-dimensional measures. As a consequence we
obtain a differentiability result for Lipschitz functions with respect to
(measures associated to) $k$-dimensional normal currents, which we use to
extend certain formulas involving normal currents and maps of class $C^1$ to
Lipschitz maps.

31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th