Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New existence theorems in measure theory and equivalence results for the
  existence of invariant probabilities   We describe a construction process of a relevant measure in any non-empty
compact metric space. This probability measure has invariance properties with
respect to isometric maps defined on open sets. These properties imply that
this measure is an appropriate generalisation of the Lebesgue one. Results
about its uniqueness are showed, and applications and complementary properties
are quickly studied. Peculiarly, we show an equivalence result in a general
framework linked with the Krylov-Bogolioubov theorem.

20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin