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Nonmeasurable products of absolutely negligible sets in uncountable solvable groups

  • Alexander Kharazishvili EMAIL logo
Published/Copyright: February 23, 2023
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Georgian Mathematical Journal
From the journal Georgian Mathematical Journal Volume 30 Issue 3

Abstract

It is shown that, for any uncountable solvable group ( G , ⋅ ) and any nonzero σ-finite left G-quasi-invariant measure μ on G, there exist two G-absolutely negligible subsets A and B of G such that the product A ⋅ B is not measurable with respect to μ.

Keywords: Solvable group; left quasi-invariant measure; absolutely negligible set; nonmeasurable set
MSC 2010: 28A05; 28A20; 28C10

Funding statement: This work was supported by Shota Rustaveli National Science Foundation of Georgia (SRNSFG), Grant FR-18-6190.

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Received: 2022-05-12
Accepted: 2022-09-21
Published Online: 2023-02-23
Published in Print: 2023-06-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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  3. On completely non-Baire unions in category bases
  4. Square-free values of n 2 + n + 1
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  7. The triharmonic equation on the Heisenberg group
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  9. Multiplicative bi-skew Jordan triple derivations on prime ∗-algebra
  10. Nonmeasurable products of absolutely negligible sets in uncountable solvable groups
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https://doi.org/10.1515/gmj-2023-2007
Keywords for this article
Solvable group; left quasi-invariant measure; absolutely negligible set; nonmeasurable set

Articles in the same Issue

  1. Frontmatter
  2. The second cohomology spaces of 𝒦(1) with coefficients in the superspace of weighted densities and deformations of the superspace of symbols on S 1|1
  3. On completely non-Baire unions in category bases
  4. Square-free values of n 2 + n + 1
  5. The stability and convergence analysis for singularly perturbed Sobolev problems with Robin type boundary condition
  6. Sign-changing solutions for parametric Neumann problems with broken symmetry and arbitrary growth
  7. The triharmonic equation on the Heisenberg group
  8. On Busemann–Feller extensions of translation invariant density differentiation bases
  9. Multiplicative bi-skew Jordan triple derivations on prime ∗-algebra
  10. Nonmeasurable products of absolutely negligible sets in uncountable solvable groups
  11. The double Fourier transform of non-Lebesgue integrable functions of bounded Hardy–Krause variation
  12. On the stochastic integral representation of Brownian functionals
  13. Generalized Bessel matrix functions
  14. Degenerate time-fractional diffusion equation with initial and initial-boundary conditions
  15. Some new characterizations of EP elements, partial isometries and strongly EP elements in rings with involution
  16. 𝐿𝑝(⋅) − 𝐿𝑞(⋅) estimates for convolution operators with singular measures supported on surfaces of half the ambient dimension
  17. Tilting pairs and Wakamatsu tilting subcategories over triangular matrix algebras
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