Thinnable Ideals and Invariance of Cluster Points release_tvz5xwwlqfd4bewcmuebaojcki

by Paolo Leonetti

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2017  

Abstract

We define a class of so-called thinnable ideals 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 I, it is shown that the set of I-cluster points of (x_n) is equal to the set of 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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Date   2017-06-24
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arXiv  1706.07954v1
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