Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hotspot lemmas for non-compact spaces   We extend the hotspot lemma, or Piatetski\u{i}-Shapiro normality criterion,
to dynamical systems on non-compact spaces. We build on the work of N. G.
Moshchevitin and I. D. Shkredov, noting an issue in some of their proofs, and
adding a necessary and sufficient condition to remove this issue.

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The categories of this paper are: stat
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
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The categories of this paper are: econ
26
The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: math-ph