Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Capacities, Measurable Selection and Dynamic Programming Part I:
  Abstract Framework   We give a brief presentation of the capacity theory and show how it derives
naturally a measurable selection theorem following the approach of Dellacherie
(1972). Then we present the classical method to prove the dynamic programming
of discrete time stochastic control problem, using measurable selection
arguments. At last, we propose a continuous time extension, that is an abstract
framework for the continuous time dynamic programming principle (DPP).

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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th