Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measurable equidecompositions for group actions with an expansion
  property   Given an action of a group $\Gamma$ on a measure space $\Omega$, we provide a
sufficient criterion under which two sets $A, B\subseteq \Omega$ are measurably
equidecomposable, i.e., $A$ can be partitioned into finitely many measurable
pieces which can be rearranged using the elements of $\Gamma$ to form a
partition of $B$. In particular, we prove that every bounded measurable subset
of $R^n$, $n\ge 3$, with non-empty interior is measurably equidecomposable to a
ball via isometries. The analogous result also holds for some other spaces,
such as the sphere or the hyperbolic space of dimension $n\ge 2$.

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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: econ