Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maps of several variables of finite total variation and Helly-type
  selection principles   Given a map from a rectangle in the n-dimensional real Euclidean space into a
metric semigroup, we introduce a concept of the total variation, which
generalizes a similar concept due to T. H. Hildebrandt (1963) for real
functions of two variables and A. S. Leonov (1998) for real functions of n
variables, and study its properties. We show that the total variation has many
classical properties of Jordan's variation such as the additivity, generalized
triangle inequality and sequential lower semicontinuity. We prove two variants
of a pointwise selection principle of Helly-type, one of which is as follows: a
pointwise precompact sequence of metric semigroup valued maps on the rectangle,
whose total variations are uniformly bounded, admits a pointwise convergent
subsequence.

23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph