## Real Analysis Exchange

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

#### 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

#### 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