• Limits of commutative triangular systems on locally compact groups

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/111/01/0049-0063

• # Keywords

Embeddable measures; triangular systems of measures; infinitesimally divisible measures; totally disconnected groups; real algebraic groups

• # Abstract

On a locally compact group G, if$$v_n^{k_n } \to \mu ,(k_n \to \infty )$$, for some probability measuresvn and μ onG, then a sufficient condition is obtained for the set$$A = \{ v_n^m \left| {m \leqslant k_n } \right.\}$$ to be relatively compact; this in turn implies the embeddability of a shift of μ. The condition turns out to be also necessary when G is totally disconnected. In particular, it is shown that ifG is a discrete linear group over R then a shift of the limit μ is embeddable. It is also shown that any infinitesimally divisible measure on a connected nilpotent real algebraic group is embeddable.

• # Author Affiliations

1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai - 400 005, India

• # Proceedings – Mathematical Sciences

Volume 132, 2022
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019