Continuous Measures on Homogenous Spaces
[Mesures continues sur des espaces homogènes]
Annales de l'Institut Fourier, Tome 59 (2009) no. 6, pp. 2169-2174.

Dans ce travail, on étend la caractérisation des mesures continues, due à Wiener, à des variétés compactes et homogènes. Pour des groupes de Lie compacts et semisimples, et pour des nilvariétés, on trouve des conditions nécessaires et suffisantes pour qu’une mesure de probabilité soit continue. Les démonstrations s’appuient sur des propriétés élémentaires des noyaux de la chaleur.

In this paper we generalize Wiener’s characterization of continuous measures to compact homogenous manifolds. In particular, we give necessary and sufficient conditions on probability measures on compact semisimple Lie groups and nilmanifolds to be continuous. The methods use only simple properties of heat kernels.

DOI : https://doi.org/10.5802/aif.2487
Classification : 60Bxx,  60B15,  30Cxx,  30C40
Mots clés : mesures de probabilités sur des groupes, noyaux de chaleur
@article{AIF_2009__59_6_2169_0,
     author = {Bj\"orklund, Michael and Fish, Alexander},
     title = {Continuous Measures  on Homogenous Spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {2169--2174},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {59},
     number = {6},
     year = {2009},
     doi = {10.5802/aif.2487},
     mrnumber = {2640917},
     zbl = {1194.60009},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.2487/}
}
Björklund, Michael; Fish, Alexander. Continuous Measures  on Homogenous Spaces. Annales de l'Institut Fourier, Tome 59 (2009) no. 6, pp. 2169-2174. doi : 10.5802/aif.2487. http://archive.numdam.org/articles/10.5802/aif.2487/

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