Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probability monads as codensity monads   We show from a categorical point of view that probability measures on certain
measurable or topological spaces arise canonically as the extension of
probability distributions on countable sets. We do this by constructing
probability monads as the codensity monads of functors that send a countable
set to the space of probability distributions on that set. On (pre)measurable
spaces we discuss monads of probability (pre)measures and their finitely
additive analogues. We also give codensity constructions for monads of Radon
measures on compact Hausdorff spaces and compact metric spaces and for the
monad of Baire measures on Hausdorff spaces.
  A crucial role in these constructions is given by integral representation
theorems, which we derive from a generalized Daniell-Stone theorem.

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
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc