Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kac's formula, vertices of chains and equidecomposability of functions
  and enhanced functions (PHD thesis)   This PHD thesis hinges on the terms mentioned in the title. It introduces a
formalism which allows one to find equalities generalizing the formula of Mark
Kac which deals with a measure-preserving transformation. The formalism is
meaningful for general measure-preserving actions of groups ("discrete",
"continuous", "multidimensional"). Some aspects of the notions introduced are
investigated.

4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
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
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph