Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solid-set functions and topological measures on locally compact spaces   A topological measure on a locally compact space is a set function on open
and closed subsets which is finitely additive on the collection of open and
compact sets, inner regular on open sets, and outer regular on closed sets.
Almost all works devoted to topological measures, corresponding non-linear
functionals, and their applications deal with compact spaces. The present paper
is one in a series that investigates topological measures and corresponding
non-linear functionals on locally compact spaces. Here we examine solid and
semi-solid sets on a locally compact space. We then give a method of
constructing topological measures from solid-set functions on a locally
compact, connected, locally connected space. The paper gives examples of finite
and infinite topological measures on locally compact, non-compact spaces and
presents an easy way to generate topological measures on spaces whose one-point
compactification has genus 0 from existing examples of topological measures on
compact spaces.

12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol