Real Analysis Exchange
- Real Anal. Exchange
- Volume 44, Number 1 (2019), 217-228.
On the Steinhaus Property and Ergodicity via the Measure-Theoretic Density of Sets
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.
Real Anal. Exchange, Volume 44, Number 1 (2019), 217-228.
First available in Project Euclid: 27 June 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05] 28D05: Measure-preserving transformations
Kharazishvili, Alexander. On the Steinhaus Property and Ergodicity via the Measure-Theoretic Density of Sets. Real Anal. Exchange 44 (2019), no. 1, 217--228. doi:10.14321/realanalexch.44.1.0217. https://projecteuclid.org/euclid.rae/1561622441