Real Analysis Exchange

Non-Linear Images of \(\mu\)-Shadings, Shadings in \(\mathbb{R}^2\), and Quotient Sets of \(\mu\)-Shadings

Keith Neu and Filip Strobin

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Abstract

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.

Article information

Source
Real Anal. Exchange, Volume 38, Number 2 (2012), 273-298.

Dates
First available in Project Euclid: 27 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.rae/1403894893

Mathematical Reviews number (MathSciNet)
MR3261878

Zentralblatt MATH identifier
1298.28008

Subjects
Primary: 28A12: Contents, measures, outer measures, capacities

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

Citation

Neu, Keith; Strobin, Filip. Non-Linear Images of \(\mu\)-Shadings, Shadings in \(\mathbb{R}^2\), and Quotient Sets of \(\mu\)-Shadings. Real Anal. Exchange 38 (2012), no. 2, 273--298. https://projecteuclid.org/euclid.rae/1403894893


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