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- W4302375910 abstract "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]." @default.
- W4302375910 created "2022-10-06" @default.
- W4302375910 creator A5008510143 @default.
- W4302375910 date "2017-06-24" @default.
- W4302375910 modified "2023-10-14" @default.
- W4302375910 title "Thinnable Ideals and Invariance of Cluster Points" @default.
- W4302375910 doi "https://doi.org/10.48550/arxiv.1706.07954" @default.
- W4302375910 hasPublicationYear "2017" @default.
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