Translator Disclaimer
2019 On the Steinhaus Property and Ergodicity via the Measure-Theoretic Density of Sets
Alexander Kharazishvili
Real Anal. Exchange 44(1): 217-228 (2019). DOI: 10.14321/realanalexch.44.1.0217

Abstract

It is shown how the Steinhaus property and ergodicity of a translation invariant extension \(\mu\) of the Lebesgue measure depend on the measure-theoretic density of \(\mu\)-measurable sets. Some connection of the Steinhaus property with almost convex sets is considered and a translation invariant extension of the Lebesgue measure is presented, for which the generalized Steinhaus property together with the mid-point convexity do not imply the almost convexity.

Citation

Download Citation

Alexander Kharazishvili. "On the Steinhaus Property and Ergodicity via the Measure-Theoretic Density of Sets." Real Anal. Exchange 44 (1) 217 - 228, 2019. https://doi.org/10.14321/realanalexch.44.1.0217

Information

Published: 2019
First available in Project Euclid: 27 June 2019

zbMATH: 07088972
MathSciNet: MR3951343
Digital Object Identifier: 10.14321/realanalexch.44.1.0217

Subjects:
Primary: 28A05, 28D05
Secondary: 26A05

Rights: Copyright © 2019 Michigan State University Press

JOURNAL ARTICLE
12 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.44 • No. 1 • 2019
Back to Top