Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigidity of amalgamated free products in measure equivalence   A discrete countable group \Gamma is said to be ME rigid if any discrete
countable group that is measure equivalent to \Gamma is virtually isomorphic to
\Gamma. In this paper, we construct ME rigid groups by amalgamating two groups
satisfying rigidity in a sense of measure equivalence. A class of amalgamated
free products is introduced, and discrete countable groups which are measure
equivalent to a group in that class are investigated.

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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: eess