Cantor set arithmetic
Jayadev S. Athreya, Bruce Reznick, Jeremy T. Tyson

TL;DR
This paper explores the algebraic and measure-theoretic properties of the Cantor set under multiplication and division, revealing that every number in [0,1] can be expressed as a product of Cantor set elements and analyzing the structure of their quotients.
Contribution
It demonstrates that any number in [0,1] can be written as a product of three Cantor set elements and characterizes the measure and structure of sets formed by products and quotients of Cantor set elements.
Findings
Every element in [0,1] can be written as x^2 y with x,y in C.
The set of products xy with x,y in C has measure between 17/21 and 8/9.
The structure of the quotient set C/C is described in detail.
Abstract
Every element of can be written in the form , where are elements of the Cantor set . 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 that can be written in the form with and in is a closed subset of with Lebesgue measure strictly between and . We also describe the structure of the quotient of by itself, that is, the image of under the function .
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