Pointwise limits for sequences of orbital integrals

• Autorzy: Claire Anantharaman-Delaroche
• Języki publikacji: EN

Abstrakty

EN

In 1967, Ross and Stromberg published a theorem about pointwise limits of orbital integrals for the left action of a locally compact group G on (G,ρ), where ρ is the right Haar measure. We study the same kind of problem, but more generally for left actions of G on any measure space (X,μ), which leave the σ-finite measure μ relatively invariant, in the sense that sμ = Δ(s)μ for every s ∈ G, where Δ is the modular function of G. As a consequence, we also obtain a generalization of a theorem of Civin on one-parameter groups of measure preserving transformations. The original motivation for the circle of questions treated here dates back to classical problems concerning pointwise convergence of Riemann sums of Lebesgue integrable functions.

Kategorie tematyczne

• 28C10: Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
• 37A15: General groups of measure-preserving transformations \SeeMainly{}
• 47A35: Ergodic theory
• 26A42: Integrals of Riemann, Stieltjes and Lebesgue type
• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 118
• Numer: 2
• Strony: 401-418

Daty

wydano

2010

Twórcy

autor

Claire Anantharaman-Delaroche

• Laboratoire de Mathématiques et Applications, Physique Mathématique d'Orléans (MAPMO - UMR6628), Fédération Denis Poisson (FDP - FR2964), CNRS/Université d'Orléans, B.P. 6759, F-45067 Orléans Cedex 2, France

Identyfikatory

DOI

10.4064/cm118-2-4