Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rectifiability and approximate differentiability of higher order for
  sets   The main goal of this paper is to develop a concept of approximate
differentiability of higher order for subsets of the Euclidean space that
allows to characterize higher order rectifiable sets, extending somehow well
known facts for functions. We emphasize that for every subset $ A $ of the
Euclidean space and for every integer $ k \geq 2 $ we introduce the approximate
differential of order $ k $ of $ A $ and we prove it is a Borel map whose
domain is a (possibly empty) Borel set. This concept could be helpful to deal
with higher order rectifiable sets in applications.

34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas