Let S be the set of subsequences (xnk) of a given real sequence (x n ) which preserve the set of statistical cluster points. It has been recently shown that S is a set of full (Lebesgue) measure. Here, on the other hand, we prove that S is meager if and only if there exists an ordinary limit point of (x n ) which is not also a statistical cluster point of (x n ). This provides a non-analogue between measure and category.

Duality between Measure and Category of Almost All Subsequences of a Given Sequence

Leonetti P
;
2019

Abstract

Let S be the set of subsequences (xnk) of a given real sequence (x n ) which preserve the set of statistical cluster points. It has been recently shown that S is a set of full (Lebesgue) measure. Here, on the other hand, we prove that S is meager if and only if there exists an ordinary limit point of (x n ) which is not also a statistical cluster point of (x n ). This provides a non-analogue between measure and category.
Asymptotic density; Meager set; Statisical limit points; Statistical cluster points
Leonetti, P; Miller, H; Miller-Wan Wieren, L
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2142082
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