On the theorem on asymptotic equidistribution of the convolution powers of symmetric measures on a~unimodular group
Matematičeskie zametki, Tome 60 (1996) no. 1, pp. 120-126.

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The theorem on the asymptotic equidistribution of the convolution powers of a symmetric probability measure given on a unimodular group [1] deals with a measure whose convolution powers, starting from one of them, load an arbitrary prescribed nonempty subset of the group. In the present note, we indicate the modifications that arise under the replacement of the above condition by the requirement that the smallest closed subgroup (of the group considered) generated by the support of this measure coincide with the group itself.
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M. G. Shur. On the theorem on asymptotic equidistribution of the convolution powers of symmetric measures on a~unimodular group. Matematičeskie zametki, Tome 60 (1996) no. 1, pp. 120-126. http://geodesic.mathdoc.fr/item/MZM_1996_60_1_a10/

[1] Shur M. G., “Asimptoticheskaya ravnoraspredelennost svertochnykh stepenei simmetrichnykh veroyatnostnykh mer na unimodulyarnykh gruppakh”, Funktsion. analiz i ego prilozh., 27:1 (1992), 92–93 | MR

[2] Avez A., “Limite de quotients pour les marches aléatoires sur les groups”, C. R. Acad. Sci. Paris, 276:4 (1973), 317–320 | MR | Zbl

[3] Khyuitt E., Ross K., Abstraktnyi garmonicheskii analiz, T. 1, Nauka, M., 1975

[4] Shur M. G., “K predelnym teoremam dlya otnoshenii, porozhdennykh sluchainymi bluzhdaniyami v odnorodnykh prostranstvakh, 1”, Teoriya veroyatn. i ee primen., 33:4 (1988), 706–719 | MR

[5] Nummelin E., Obschie neprivodimye tsepi Markova i neotritsatelnye operatory, Mir, M., 1989

[6] Revuz D., Markov chains, North-Holland, Amsterdam–N.Y., 1975 | Zbl