Cantor Set Arithmetic

被引：21

作者：

Athreya, Jayadev S. ^{[1
]}

Reznick, Bruce ^{[2
]}

Tyson, Jeremy T. ^{[2
]}

机构：

[1] Univ Washington, Dept Math, Seattle, WA 98195 USA

[2] Univ Illinois, Dept Math, Urbana, IL 61801 USA

来源：

AMERICAN MATHEMATICAL MONTHLY | 2019年 / 126卷 / 01期

关键词：

MSC: Primary 28A80; Secondary; 11K55; SUMS;

D O I：

10.1080/00029890.2019.1528121

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Every element u of can be written in the form , where x, y are elements of the Cantor set C. In particular, every real number between zero and one is the product of three elements of the Cantor set. On the other hand, the set of real numbers v that can be written in the form v = xy with x and y in C is a closed subset of with Lebesgue measure strictly between and . We also describe the structure of the quotient of C by itself, that is, the image of under the function x/y.

引用

页码：4 / 17

页数：14

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