Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonmeasurable subgroups of compact groups   In 1985 S.~Saeki and K.~Stromberg published the following question: {\it Does
every infinite compact group have a subgroup which is not Haar measurable?} An
affirmative answer is given for all compact groups with the exception of some
metric profinite groups known as strongly complete. In this spirit it is also
shown that every compact group contains a non-Borel subgroup.

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The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: adap-org
9
The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph