Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An abstract decomposition of measures and its many applications   We consider a little-known abstract decomposition result, due to Dellacherie,
and show that it yields many decompositions of measures, several of which are
new. Then, we investigate how the outputs of the decomposition depend on its
inputs, in particular characterising the two elements of the decomposition as
projections in the sense of Riesz spaces and of metric spaces.

14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin