A note on the convolution of probability measures

Caby, Errol

doi:10.1090/S0002-9939-1987-0875395-9

A note on the convolution of probability measures
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by Errol Caby

Proc. Amer. Math. Soc. 99 (1987), 549-554

DOI: https://doi.org/10.1090/S0002-9939-1987-0875395-9

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Abstract:

Simple proofs of the continuity of the convolution of measures for certain topologies are presented. In addition, results on the compactness of probability measures and on infinite convolutions of probability measures are obtained.

References

Errol Caby, The weak convergence of uniform measures, J. Multivariate Anal. 9 (1979), no. 1, 130–137. MR 530644, DOI 10.1016/0047-259X(79)90071-X
Errol Caby, Extension of uniform measures, Proc. Amer. Math. Soc. 89 (1983), no. 3, 433–439. MR 715861, DOI 10.1090/S0002-9939-1983-0715861-6
I. Csiszár, On infinite products of random elements and infinite convolutions of probability distributions on locally compact groups, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 5 (1966), 279–295. MR 205306, DOI 10.1007/BF00535358
I. Csiszár, Some problems concerning measures on topological spaces and convolutions of measures on topological groups, Les probabilités sur les structures algébriques (Actes Colloq. Internat. CNRS, No. 186, Clermont-Ferrand, 1969) Éditions Centre Nat. Recherche Sci., Paris, 1970, pp. 75–96 (English, with French summary). MR 0420768
I. Csiszár, On the weak* continuity of convolution in a convolution algebra over an arbitrary topological group, Studia Sci. Math. Hungar. 6 (1971), 27–40. MR 288599
Zdeněk Frolík, Mesures uniformes, C. R. Acad. Sci. Paris Sér. A-B 277 (1973), A105–A108 (French). MR 323984
Zdeněk Frolík, Représentation de Riesz des mesures uniformes, C. R. Acad. Sci. Paris Sér. A-B 277 (1973), A163–A166 (French). MR 323985
Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496
L. Le Cam, Remarques sur le théorème limite central dans les espaces localement convexes, Les probabilités sur les structures algébriques (Actes Colloq. Internat. CNRS, No. 186, Clermont-Ferrand, 1969) Éditions Centre Nat. Recherche Sci., Paris, 1970, pp. 233–249 (French, with English summary). Avec commentaire en anglais par R. M. Dudley. MR 0410832

Note on a certain class of measures

K. R. Parthasarathy, Probability measures on metric spaces, Probability and Mathematical Statistics, No. 3, Academic Press, Inc., New York-London, 1967. MR 0226684
A. Tortrat, Lois de probabilité sur un espace topologique complètement régulier et produits infinis à termes indépendants dans un groupe topologique, Ann. Inst. H. Poincaré Sect. B 1 (1964/1965), 217–237 (French). MR 0178498

Lois tendues et convolutions démombrables dans un groupe topologique

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