Limit theorems for measures on nonmetrizable locally compact abelian groups

Author:
David C. Bossard

Journal:
Trans. Amer. Math. Soc. **159** (1971), 185-205

MSC:
Primary 60.08

DOI:
https://doi.org/10.1090/S0002-9947-1971-0279845-3

MathSciNet review:
0279845

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Abstract | References | Similar Articles | Additional Information

Abstract: In a recent book, Parthasarathy provides limit theorems for sums of independent random variables defined on a metrizable locally compact abelian group. These results make heavy use of the metric assumption. This paper consists of a reworking of certain results contained in Parthasarathy to see what can be done without the metric restriction. Among the topics considered are: necessary and sufficient conditions for a limit law to have an idempotent factor; the relationship between limits of compound Poisson laws and limits of sums of independent random variables; and a representation theorem for certain limit laws.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1971-0279845-3

Keywords:
Locally compact groups,
nonmetrizable spaces,
Prokhorov Theorem,
conditional compactness of measures,
probability measures,
limit theorems,
infinitesimal arrays,
triangular arrays,
infinitely divisible distributions,
idempotent measures,
characteristic functions,
representation theorems,
compound Poisson laws

Article copyright:
© Copyright 1971
American Mathematical Society