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2018 Thinnable ideals and invariance of cluster points
Paolo Leonetti
Rocky Mountain J. Math. 48(6): 1951-1961 (2018). DOI: 10.1216/RMJ-2018-48-6-1951

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 of its subsequences, in the sense of Lebesgue measure. Lastly, we obtain a characterization of ideal convergence, which improves the main result in Miller 1995 (MR1260176).

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Paolo Leonetti. "Thinnable ideals and invariance of cluster points." Rocky Mountain J. Math. 48 (6) 1951 - 1961, 2018. https://doi.org/10.1216/RMJ-2018-48-6-1951

Information

Published: 2018
First available in Project Euclid: 24 November 2018

zbMATH: 06987234
MathSciNet: MR3879311
Digital Object Identifier: 10.1216/RMJ-2018-48-6-1951

Subjects:
Primary: 40A35
Secondary: 11B05, 54A20

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 6 • 2018
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