Abstract
Khinchin's theorem on the infinite divisibility of the limit of an infinitesimal triangular array of distributions is extended to distributions on a broad class of groups.
Similar content being viewed by others
References
Khinchin, A. Ya. (1938).Limit Laws for Sums of Independent Random Variables, ONTI, Moscow-Leningrad.
Parthasarathy, K. R., Ranga Rao, R., and Varadhan, S. R. S. (1963). Probability distributions on locally compact Abelian groups,Ill. J. Math. 7, 337–369.
Heyer, H. (1977).Probability Measures on Locally Compact Groups, Springer, New York.
Ruzsa, I. Z. Infinite divisibility I, to appear inAdv. Math.
Davidson, R. (1969). More Delphic theory and practice,Z. Wahrsch. verw. Geb 13, 191–203.
Ruzsa, I. Z., and Székely, G. J. (1985). Theory of decomposition in semigroups,Adv. Math. 56, 9–27.
Ruzsa, I. Z., and Székely, G. J. (1982). Decomposition of probability measures on groups, inProbability Measures on Groups (Proc. Conf. Oberwolfach 1981), Lecture Notes in Mathematics 928, Springer, New York, pp. 409–417.
Ruzsa, I. Z., and Székely, G. J. (1986). A note on our paper “Theory of decomposition in semigroups,”Adv. Math. 60, 235–236.
Ruzsa, I. Z. (1983). Infinite convolution and shift-convergence of measures on topological groups, inProbability Measures on Groups (Proc. Conf. Oberwolfach 1983), Lecture Notes in Mathematics 1064, Springer, New York, pp. 409–417.
Linnik, Yu. V., and Ostrovskii, I. V. (1977).Decomposition of Random Variables and Vectors, Trans. of Mathematics Monographs, 48, American Mathematical Society, Providence, Rhode Island (Russian ed., Nauka, Moscow, 1972).
Billingsley, P. (1968).Convergence of Probability Measures, Wiley, New York.
Štěpan, J. (1970). On the family of translations of a tight probability measure on a topological group,Z. Wahrsch. verw. Geb. 15, 131–138.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ruzsa, I.Z. Infinite divisibility II. J Theor Probab 1, 327–339 (1988). https://doi.org/10.1007/BF01048723
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01048723