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Article Dans Une Revue Colloquium Mathematicum Année : 2010

Pointwise limits for sequences of orbital integrals

Résumé

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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Dates et versions

hal-00360349 , version 1 (11-02-2009)

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