Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the isomorphism problem for measures on Boolean algebras   The paper investigates possible generalisations of Maharam's theorem to a
classification of Boolean algebras that support a finitely additive measure. We
prove that Boolean algebras that support a finitely additive non-atomic
uniformly regular measure are metrically isomorphic to a subalgebras of the
Jordan algebra with the Lebesgue measure. We give some partial analogues to be
used for a classification of algebras that support a finitely additive
non-atomic measure with a higher uniform regularity number. We show that some
naturally induced equivalence relations connected to metric isomorphism are
quite complex even on the Cantor algebra and therefore probably we cannot hope
for a nice general classification theorem for finitely--additive measures.
  We present an example of a Boolean algebra which supports only separable
measures but no uniformly regular one.

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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn