• Riddhi Shah

      Articles written in Proceedings – Mathematical Sciences

    • Limits of commutative triangular systems on locally compact groups

      Riddhi Shah

      More Details Abstract Fulltext PDF

      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.

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