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arXiv · 1711.04265

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

Paolo Leonetti·Harry Miller·Leila Miller-Van Wieren
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Abstract

Let $S$ be the set of subsequences $(x_{n_k})$ 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 a statistical cluster point of $(x_n)$. This provides a non-analogue between measure and category.

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BibTeXRIS

Paolo Leonetti, Harry Miller, Leila Miller-Van Wieren. 2017-11-12. Duality between Measure and Category of Almost All Subsequences of a Given Sequence. https://arxiv.org/abs/1711.04265

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