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Some inequalities that arise in measure theory

Part of: Abstract harmonic analysis Inequalities

Published online by Cambridge University Press:  09 April 2009

Gavin Brown
Gavin Brown
Affiliation:
School of MathematicsUniversity of New South WalesKensington, N.S.W. 2033, Australia
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Abstract

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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.

MSC classification

Secondary: 26D20: Other analytical inequalities 43A05: Measures on groups and semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 45 , Issue 1 , August 1988 , pp. 83 - 94
Copyright
Copyright © Australian Mathematical Society 1988

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