非分布序列集的拓扑性质

Pub Date : 2020-11-01 DOI:10.2478/ausm-2020-0018

József Bukor, J. Tóth

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引用次数: 0

摘要

如果对于任意非空区间I，集{n∈𝕅:xn∈I}具有上渐近密度1，则实序列(xn)是非分布的。这篇笔记的主要结论是，所有非分布实序列的集合是所有实序列集合中的残集(即，非分布是贝尔范畴意义上的一个典型性质)。我们也推广了这个结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On topological properties of the set of maldistributed sequences

Abstract The real sequence (xn) is maldistributed if for any non-empty interval I, the set {n ∈𝕅 : xn ∈I} has upper asymptotic density 1. The main result of this note is that the set of all maldistributed real sequences is a residual set in the set of all real sequences (i.e., the maldistribution is a typical property in the sense of Baire categories). We also generalize this result.

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