Pointwise limits for sequences of orbital integrals

Claire Anantharaman-Delaroche. "Pointwise limits for sequences of orbital integrals." Colloquium Mathematicae 118.2 (2010): 401-418. <http://eudml.org/doc/284369>.

@article{ClaireAnantharaman2010,
abstract = {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.},
author = {Claire Anantharaman-Delaroche},
journal = {Colloquium Mathematicae},
keywords = {Haar measure; locally compact group; modular function},
language = {eng},
number = {2},
pages = {401-418},
title = {Pointwise limits for sequences of orbital integrals},
url = {http://eudml.org/doc/284369},
volume = {118},
year = {2010},
}

TY - JOUR
AU - Claire Anantharaman-Delaroche
TI - Pointwise limits for sequences of orbital integrals
JO - Colloquium Mathematicae
PY - 2010
VL - 118
IS - 2
SP - 401
EP - 418
AB - 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.
LA - eng
KW - Haar measure; locally compact group; modular function
UR - http://eudml.org/doc/284369
ER -