# Limits of commutative triangular systems on locally compact groups

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## Abstract

On a locally compact group G, if\(v_n^{k_n } \to \mu ,(k_n \to \infty )\), for some probability measures*v* _{n} and μ on*G*, 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 if*G* 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.

## Keywords

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

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