Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An application of Shoenfield's absoluteness theorem to the theory of
  uniform distribution   If (B_x: x in N) is a Borel family of sets, indexed by the Baire space N =
omega^omega, all B_x have measure zero, and the family is increasing, then the
union of all B_x also has measure zero. We give two proofs of this theorem: one
in the language of set theory, using Shoenfield's theorem on Sigma-1-2 sets,
the other in the language of probability theory, using von Neumann's selection
theorem, and we apply the theorem to a question on completely uniformly
distributed sequences.

25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin