Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Haar-open sets: a right way of generalizing the Steinhaus sum theorem to
  non-locally compact groups   Let $X$ be the countable product of Abelian locally compact Polish groups and
$A,B\subset X$ be two Borel sets, which are not Haar-null in $X$. We prove that
the sum-set $A+B:=\{a+b:a\in A,\;\;b\in B\}$ is Haar-open in the sense that for
any non-empty compact subset $K\subset X$ and point $p\in K$ there exists a
point $x\in X$ such that the set $K\cap(A+B+x)$ is a neighborhood of $p$ in
$K$. This is a generalization of the classical Steinhaus Theorem (1920) to
non-locally compact groups. We do not know if this generalization holds for
Banach spaces.

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The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: stat