集维为零的中心康托集族

Q4 Mathematics Tatra Mountains Mathematical Publications Pub Date : 2021-10-01 DOI:10.2478/tmmp-2021-0001

P. Nowakowski

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引用次数: 1

摘要

在M. Balcerzak, T. Filipczak和P. Nowakowski最近的一篇文章中，我们用概率积测度µ在波兰空间X: = (0,1) n上识别了[0,1]的中心Cantor子集CS族。研究了CS中集族P0的大小。我们证明了P0是微测度零的，而它被看作x的相应子集。我们还检查了P0和其他由小集合组成的子族CS之间可能存在的包含。

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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The Family of Central Cantor Sets with Packing Dimension Zero

Abstract As in the recent article of M. Balcerzak, T. Filipczak and P. Nowakowski, we identify the family CS of central Cantor subsets of [0, 1] with the Polish space X : = (0, 1)ℕ equipped with the probability product measure µ. We investigate the size of the family P0 of sets in CS with packing dimension zero. We show that P0 is meager and of µ measure zero while it is treated as the corresponding subset of X. We also check possible inclusions between P0 and other subfamilies CS consisting of small sets.

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Tatra Mountains Mathematical Publications Mathematics-Mathematics (all)

CiteScore

1.00

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0.00%

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