Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Category of Probability Spaces   We introduce a category Prob of probability spaces whose objects are all
probability spaces and arrows are corresponding to measurable functions
satisfying an absolutely continuous requirement. We can consider a Prob-arrow
as an evolving direction of information with a way of its interpretation. We
introduce a contravariant functor E from Prob to Set, the category of sets. The
functor E provides conditional expectations along arrows in Prob, which are
generalizations of the classical conditional expectations. For a Prob arrow f,
we introduce two concepts f-measurability and f-independence and investigate
their interaction with conditional expectations along f. We also show that the
completion of probability spaces is naturally formulated as an endofunctor of
Prob.

7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg