Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On interval based generalizations of absolute continuity for functions
  on $\mathbb{R}^n$   We study notions of absolute continuity for functions defined on
$\mathbb{R}^n$similar to the notion of $\alpha$-absolute continuity in the
sense of Bongiorno. We confirm a conjecture of Mal\'y that 1-absolutely
continuous functions do not need to be differentiable a.e., and we show several
other pathological examples of functions in this class. We establish
containment relations of the class $1-AC_{\rm WDN}$ which consits of all
functions in $1-AC$ which are in the Sobolev space $W^{1,2}_{loc}$, are
differentiable a.e. and satisfy the Luzin (N) property, with previously studied
classes of absolutely continuous functions.

37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics