Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thinnable Ideals and Invariance of Cluster Points   We define a class of so-called thinnable ideals $\mathcal{I}$ on the positive
integers which includes several well-known examples, e.g., the collection of
sets with zero asymptotic density, sets with zero logarithmic density, and
several summable ideals. Given a sequence $(x_n)$ taking values in a separable
metric space and a thinnable ideal $\mathcal{I}$, it is shown that the set of
$\mathcal{I}$-cluster points of $(x_n)$ is equal to the set of
$\mathcal{I}$-cluster points of almost all its subsequences, in the sense of
Lebesgue measure. Lastly, we obtain a characterization of ideal convergence,
which improves the main result in [Trans. Amer. Math. Soc. 347 (1995),
1811--1819].

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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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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: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: ao-sci