Some inequalities that arise in measure theory

Journal of the Australian Mathematical Society

Gavin Brown¹ 

关键词: primary 26 D 20;    secondary 43 A 05;    43 A 10;   

DOI  :  10.1017/S1446788700032298

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

The Lebesgue measure, λ (E + F), of the algebraic sum of two Borel sets, E, F of the classical “middle-thirds’ Cantor set on the circle can be estimated by evaluating the Cantor meaure, μ of the summands. For example log λ (E + F) exceeds a fixed scalar multiple of log μ (E)+ log μ (F). Several numerical inequalities which are required to prove this and related results look tantalizingly simple and basic. Here we isolate them from the measure theory and present a common format and proof.

【 授权许可】

Unknown