Geodesic
Three-series theorems for locally compact groups
Sbornik. Mathematics, Tome 45 (1983) no. 2, pp. 225-241 
V. M. Maksimov. Three-series theorems for locally compact groups. Sbornik. Mathematics, Tome 45 (1983) no. 2, pp. 225-241. http://geodesic.mathdoc.fr/item/SM_1983_45_2_a4/
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     author = {V. M. Maksimov},
     title = {Three-series theorems for locally compact groups},
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     volume = {45},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_45_2_a4/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

This article deals with conditions for the convergence of the product $\prod\limits_1^\infty\xi_n$ of independent random variables $\xi_n$ taking values in an arbitrary locally compact group $G$. For various types of groups necessary and sufficient conditions are given for the convergence of this product almost everywhere, expressed in terms of the group $G$. They can be regarded as analogues of the classical three-series theorem. Bibliography: 14 titles

[1] Heyer H., Probability measures on locally compact groups, Springer-Verlag, Berlin–Heidelberg–New York, 1977 | MR | Zbl

[2] Lévy P., “L'addition des variables aléatoires définies sur une circonférence”, Bull. Soc. Math. France, 67 (1939), 1–41 | MR | Zbl

[3] Maksimov V. M., “Matematicheskie ozhidaniya dlya veroyatnostnykh raspredelenii na kompaktnykh gruppakh i ikh primenenie”, DAN SSSR, 203:3 (1972), 524–527 | MR | Zbl

[4] Maksimov V. M., “Mathematical expectations for probability distributions on compact groups”, Math. Z., 174 (1980), 49–60 | DOI | MR | Zbl

[5] Maksimov V. M., “Printsip skhodimosti “pochti vsyudu” v gruppakh”, Matem. sb., 91 (133) (1973), 523–536 | MR | Zbl

[6] Skorokhod T. A., “Skhodimost beskonechnykh proizvedenii sluchainykh matrits”, Teoriya sluchainykh protsessov, vyp. 5, Naukova dumka, Kiev, 1977, 86–92

[7] Ito K., Veroyatnostnye protsessy, IL, M., 1960

[8] Csiszar J., “On infinite products of random elements and infinite convolutions of probability distributions on locally compact groups”, Z. W-theorie, 5 (1966), 279–295 | MR | Zbl

[9] Tortrat A., “Lois de probabilité sur un espace topologique comoletément régulier et produits infinis à termes independants dans un groupe topologique”, Ann. Inst. H. Poincaré, Sect. B, 1:3 (1965), 217–237 | MR | Zbl

[10] Maksimov V. M., “Rasprostranenie teoremy K. Ito “o nezavisimosti skachkov protsessa” na protsessy s nezavisimymi prirascheniyami, zadannye na topologicheskikh gruppakh so schetnoi bazoi”, DAN SSSR, 182:1 (1968), 38–41 | MR | Zbl

[11] Prokhorov Yu. V., “Skhodimost sluchainykh protsessov i predelnye teoremy teorii veroyatnostei”, Teoriya veroyatn., 1:2 (1956), 177–238 | MR

[12] Glushkov V. M., “Stroenie lokalno bikompaktnykh grupp i pyataya problema Gilberta”, UMN, 12:2 (1957), 3–41 | MR | Zbl

[13] Serr Zh.-P., Algebry Li i gruppy Li, Mir, M., 1969 | MR | Zbl

[14] Maksimov V. M., “K teorii dispersii dlya veroyatnostnykh raspredelenii na kompaktnykh gruppakh”, DAN SSSR, 192:4 (1970), 732–735 | MR | Zbl