Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measure Recognition Problem   This is an article in mathematics, specifically in set theory. On the example
of the Measure Recognition Problem (MRP) the article highlights the phenomenon
of the utility of a multidisciplinary mathematical approach to a single
mathematical problem, in particular the value of a set-theoretic analysis. MRP
asks if for a given Boolean algebra $\algB$ and a property $\Phi$ of measures
one can recognize by purely combinatorial means if $\algB$ supports a strictly
positive measure with property $\Phi$. The most famous instance of this problem
is MRP(countable additivity), and in the first part of the article we survey
the known results on this and some other problems. We show how these results
naturally lead to asking about two other specific instances of the problem MRP,
namely MRP(nonatomic) and MRP(separable). Then we show how our recent work D\v
zamonja and Plebanek (2006) gives an easy solution to the former of these
problems, and gives some partial information about the latter. The long term
goal of this line of research is to obtain a structure theory of Boolean
algebras that support a finitely additive strictly positive measure, along the
lines of Maharam theorem which gives such a structure theorem for measure
algebras.

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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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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: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: stat