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    • Limits of commutative triangular systems on locally compact groups

      Riddhi Shah

      Volume 111 Issue 1 February 2001 pp 49-63

    • Fulltext

       

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      Permanent link:
      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

       

      Riddhi Shah1

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

    • Dates

       
      Published
      February 2001
      Manuscript received
      22 December 1999
      Manuscript revised
      28 July 2000

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