Nous donnons des critères pour la continuité absolue mutuelle et pour la singularité des produits de Riesz sur les groupes abéliens localement compacts. La première partie définit une telle mesure d’une manière plus générale que la définition usuelle. La deuxième partie fournit trois conditions suffisantes pour qu’un produit de Riesz soit absolument continu par rapport à un autre. Un de nos résultats contient un théorème de Brown-Moran-Ritter comme cas spécial. La dernière partie traite des produits de Riesz aléatoires. Nous établissons une certaine dichotomie probabiliste pour de telles mesures.
We give some criteria for mutual absolute continuity and for singularity of Riesz product measures on locally compact abelian groups. The first section gives the definition of such a measure which is more general than the usual definition. The second section provides three sufficient conditions for one Riesz product measure to be absolutely continuous with respect to another. One of our results contains a theorem of Brown-Moran-Ritter as a special case. The final section deals with random Riesz product measures. We shall establish a certain probabilistic dichotomy for such measures.
@article{AIF_1988__38_2_63_0,
author = {Kilmer, Shelby J. and Saeki, Sadahiro},
title = {On Riesz product measures; mutual absolute continuity and singularity},
journal = {Annales de l'Institut Fourier},
volume = {38},
year = {1988},
pages = {63-93},
doi = {10.5802/aif.1135},
mrnumber = {90a:42006},
zbl = {0633.43001},
mrnumber = {949011},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_1988__38_2_63_0}
}
Kilmer, Shelby J.; Saeki, Sadahiro. On Riesz product measures; mutual absolute continuity and singularity. Annales de l'Institut Fourier, Tome 38 (1988) pp. 63-93. doi : 10.5802/aif.1135. http://gdmltest.u-ga.fr/item/AIF_1988__38_2_63_0/
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