# Pointwise limits for sequences of orbital integrals

Abstract : In 1967, Ross and Strömberg published a theorem about pointwise limits of orbital integrals for the left action of a locally compact group $G$ onto $(G,\rho)$, where $\rho$ is the right Haar measure. In this paper, we study the same kind of problem, but more generally for left actions of $G$ onto any measured space $(X,\mu)$, which leaves the $\sigma$-finite measure $\mu$ relatively invariant, in the sense that $s\mu = \Delta(s)\mu$ for every $s\in G$, where $\Delta$ is the modular function of $G$. As a consequence, we also obtain a generalization of a theorem of Civin, relative to 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 relative to Lebesgue integrable functions.
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Cited literature [11 references]

https://hal.archives-ouvertes.fr/hal-00360349
Contributor : Claire Anantharaman-Delaroche <>
Submitted on : Wednesday, February 11, 2009 - 10:07:36 AM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
Document(s) archivé(s) le : Tuesday, June 8, 2010 - 6:32:43 PM

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Orb-Int.pdf
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• HAL Id : hal-00360349, version 1
• ARXIV : 0902.1870

### Citation

Claire Anantharaman-Delaroche. Pointwise limits for sequences of orbital integrals. Colloquium Mathematicum, 2010, 118, pp.401-418. ⟨hal-00360349⟩

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