Real Analysis Exchange

On selectors nonmeasurable with respect to quasiinvariant measures

Aleksander B. Kharazishvili

Full-text: Open access

Abstract

We discuss a question on the existence of partial \(\mu\)-nonmeasurable \(H\)-selectors, where \(\mu\) is a given nonzero \(\sigma\)-finite measure defined on some \(\sigma\)-algebra of subsets of a set \(E\) and quasiinvariant under an uncountable group \(G\) of transformations of \(E\), and \(H\) is an arbitrary countable subgroup of \(G\).

Article information

Source
Real Anal. Exchange, Volume 22, Number 1 (1996), 177-183.

Dates
First available in Project Euclid: 1 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1338515213

Mathematical Reviews number (MathSciNet)
MR1433606

Zentralblatt MATH identifier
0879.28028

Subjects
Primary: 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]
Secondary: 28A20: Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence

Keywords
transformation group quasiinvariant measure nonmeasurable selector

Citation

Kharazishvili, Aleksander B. On selectors nonmeasurable with respect to quasiinvariant measures. Real Anal. Exchange 22 (1996), no. 1, 177--183. https://projecteuclid.org/euclid.rae/1338515213


Export citation

References

  • J. Cichoń, A. B. Kharazishvili and B. Weglorz, On sets of Vitali's type, Proc. Amer. Math. Soc., 118 (1993), 1221–1228.
  • P. Erdös and R. D. Mauldin, The nonexistence of certain invariant measures, Proc. Amer. Math. Soc., 59 (1976), 321–322.
  • A. B. Kharazishvili, Certain types of invariant measures, Dokl. Akad. Nauk SSSR, 222(3) (1975), 538–540, (in Russian).
  • A. B. Kharazishvili, Some applications of Hamel bases, Bull. Acad. Sci. Georgian SSR, 85(1) (1977), 17–20 (in Russian).
  • A. B. Kharazishvili, Martin's axiom and $\Gamma$-selectors, Bull. Acad. Sci. Georgian SSR, 137(2) (1990),(in Russian).
  • A. B. Kharazishvili, Selected Topics of Point Set Theory, \Lódź University Press, \Lódź, 1996.
  • C. Ryll-Nardzewski and R. Telgarsky, The nonexistence of universal invariant measures, Proc. Amer. Math. Soc., 69 (1978), 240–242.
  • S. Solecki, On sets nonmeasurable with respect to invariant measures, Proc. Amer. Math. Soc., 119(1) (1993), 115–124.
  • S. Solecki, Measurability properties of sets of Vitali's type, Proc. Amer. Math. Soc., 119(3) (1993), 897–902.
  • S. Ulam, Zur Masstheorie in der allgemeinen Mengenlehre, Fund. Math., 16 (1930), 140–150.
  • G. Vitali, Sul Problema della Misura dei Gruppi di Punti di una Retta, Bologna, Italy, 1905.