Limits of commutative triangular systems on real and p-adic groups
Published online by Cambridge University Press: 24 October 2008
Extract
A fundamental theorem of Khinchin says that every limit of an infinitesimal triangular system of probability measures on R is infinitely divisible. This was generalized to all divisible locally compact second countable abelian groups by Parthasarathy et al. (cf. [PRV]). Recently, Ruzsa eliminated the second countability condition and also proved the theorem for all Banach spaces (cf. [R2]). A similar theorem was also proved by Gangolli for certain symmetric spaces (cf. [G]). A result of Carnal shows that infinite divisibility of limits holds for commutative infinitesimal triangular systems on compact groups (cf. [C]). The same was recently proved by Neuenschwander for simply connected step-2 nilpotent Lie groups, provided the system is symmetric or supported on a discrete subgroup (cf. [N]).
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 1 , July 1996 , pp. 181 - 192
- Copyright
- Copyright © Cambridge Philosophical Society 1996
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