Borel complexity of the set of typical numbers

被引：1
|
作者：
Tomaszewski, Jakub [1 ]
机构：
[1] AGH Univ Krakow, Fac Appl Math, Mickiewicza 30, PL-30059 Krakow, Poland
来源：
TOPOLOGY AND ITS APPLICATIONS | 2024年 / 345卷
关键词：
Typical numbers; Normal numbers; Borel hierarchy;
D O I：
10.1016/j.topol.2024.108836
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the present note we study the interrelations between the sets of so-called typical numbers and numbers that are normal in base two. Employing results by Nakai and Shiokawa, we exhibit examples of numbers that belong to one set but do not belong to the other and vice versa. Moreover, we demonstrate that the set of typical numbers is fi03 in the Borel hierarchy, i.e., it can be expressed as the intersection of countably many F sigma-sets. Using the result by Ki and Linton that asserts the same for normal numbers, we examine the Borel complexity of the set of typical numbers that are not normal, proving that it is a D2(fi03) set. (c) 2024 Elsevier B.V. All rights reserved.
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页数：12
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