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2012/2013 Non-Linear Images of \(\mu\)-Shadings, Shadings in \(\mathbb{R}^2\), and Quotient Sets of \(\mu\)-Shadings
Keith Neu, Filip Strobin
Real Anal. Exchange 38(2): 273-298 (2012/2013).


In the paper we prove that some natural modifications (for instance, images under some functions, Cartesian products, quotient sets) of certain types of \(\mu\)-shadings (or shadings), are other examples of \(\mu\)-shadings (or shadings). The studies of shadings and \(\mu\)-shadings were initiated by R. Mabry in 1990. Our work is a continuation of his and K. Neu's research in this field. In particular, we solve one problem posed by R. Mabry.


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Keith Neu. Filip Strobin. "Non-Linear Images of \(\mu\)-Shadings, Shadings in \(\mathbb{R}^2\), and Quotient Sets of \(\mu\)-Shadings." Real Anal. Exchange 38 (2) 273 - 298, 2012/2013.


Published: 2012/2013
First available in Project Euclid: 27 June 2014

zbMATH: 1298.28008
MathSciNet: MR3261878

Primary: 28A12

Keywords: almost invariance , almost isometry-invariant , almost translation-invariant , Archimedean set , Banach measure , Hamel basis , Lebesgue measure , quotient set , shade-almost invariance , shading , sum set

Rights: Copyright © 2012 Michigan State University Press

Vol.38 • No. 2 • 2012/2013
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