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A note on the equation λ * ρ * μ = ρ

Published online by Cambridge University Press:  17 April 2009

C. Robinson Edward Raja
C. Robinson Edward Raja
Affiliation:
Université d'AngersFaculté des Sciences, Départment de Mathématiques, 49045 Angers Cedex 01, France e-mail: [email protected]
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Abstract

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Let G be a Hausdorff topological group and μ and λ be probability measures on G. We prove necessary and sufficient conditions for the existence of a probability measure ρ such that λ * ρ * μ = ρ under certain conditions. We prove a similar result for probability measures on semigroups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 3 , June 1999 , pp. 421 - 426
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Bartoszek, W., ‘Concentrated probabilities’, Ann. Polon. Math. 61 (1995), 635–640.CrossRefGoogle Scholar
[2]Bartoszek, W., ‘More on the equation λ * ρ * μ = ρ’, Demonstratio Math. 29 (1996), 807–811.Google Scholar
[3]Bougerol, P., Une majoration universelle des fonctions de concentration, Lecture Notes in Math. 708 (Springer-Verlag, Berlin, Heidelberg, New York, 1979), pp. 36–40.Google Scholar
[4]Deriennic, Y. and Lin, M., ‘Convergence of iterates of averages of certain operator representations and of convolution powers’, J. Funct. Anal. 85 (1989), 86–102.CrossRefGoogle Scholar
[5]Dani, S.G. and Raja, C.R.E., ‘A note on Tortrat groups’, J. Theoret. Probab. 11 (1998), 571–576.CrossRefGoogle Scholar
[6]Eisele, P., ‘On shifted convolution powers of probability measure’, Math. Z. 211 (1992), 557–574.CrossRefGoogle Scholar
[7]Eisele, P., ‘Tortrat groups-groups with a nice behavior for sequences of shifted convolution powers’, J. Theoret. Probab. 6 (1993), 671–691.CrossRefGoogle Scholar
[8]Heyer, H., Probability measures on locally compact groups (Springer-Verlag, Berlin, Heidelberg, New York, 1976).Google Scholar
[9]Högnäs, G. and Mukherjea, A., Probability measures on semigroups (Plenum Press, New York, 1991).Google Scholar
[10]Parthasarathy, K.R., Probability measures on metric spaces (Academic Press, New York, London, 1967).CrossRefGoogle Scholar
[11]Siebert, E., ‘Convergence and convolutions of probability measures on a topological group’, Ann. Probab. 4 (1976), 433–443.CrossRefGoogle Scholar
[12]Szekely, G.J. and Zeng, W.B., ‘The Choquet-Deny convolution equation μ = μ* σ for probability measures on abelian semigroups’, J. Theoret. Probab. 3 (1990), 361–365.CrossRefGoogle Scholar
[13]Tortrat, A., ‘Lois de probabilité sur un espace topologique complètement régulier et pro-duits infinis à terms indp´endants dans un groupe topologique’, Ann. Inst. H. Poincaré Sect. B 1 (1964/1965), 217–237.Google Scholar
[14]Wójcicka, M., ‘The space of probability measures on Prohorov space is Prohorov’, Bull. Polish Acad. Sci. Math. 35 (1987), 809–811.Google Scholar