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On systems of imprimitivity on locally compact abelian groups with dense actions

J. Mathew; M. G. Nadkarni — 1978

Annales de l'institut Fourier

Consider the four pairs of groups $(Γ, R)$ , $(Γ / Γ_{0}, R / Γ_{0})$ , $(K \cap S, P)$ and $(S, B)$ , where $Γ$ , $R$ are locally compact second countable abelian groups, $Γ$ is a dense subgroup of $R$ with inclusion map from $Γ$ to $R$ continuous; $Γ_{0} \subseteq Γ \subseteq R$ is a closed subgroup of $R$ ; $S$ , $B$ are the duals of $R$ and $Γ$ respectively, and $K$ is the annihilator of $Γ_{0}$ in $B$ . Let the first co-ordinate of each pair act on the second by translation. We connect, by a commutative diagram, the systems of imprimitivity which arise in a natural fashion on each pair, starting with a system...

On sequences of σ-algebras

M. G. Nadkarni; D. Ramachandran; K. P. S. Bhaskara-Rao — 1975

Colloquium Mathematicae

Sets with doubleton sections, good sets and ergodic theory

A. Kłopotowski; M. G. Nadkarni; H. Sarbadhikari; S. M. Srivastava — 2002

Fundamenta Mathematicae

A Borel subset of the unit square whose vertical and horizontal sections are two-point sets admits a natural group action. We exploit this to discuss some questions about Borel subsets of the unit square on which every function is a sum of functions of the coordinates. Connection with probability measures with prescribed marginals and some function algebra questions is discussed.

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On systems of imprimitivity on locally compact abelian groups with dense actions

On sequences of σ-algebras

Sets with doubleton sections, good sets and ergodic theory