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Densities on locally compact abelian groups

I. D. Berg;  L. A. Rubel — 1969

Annales de l'institut Fourier

A density on a locally compact Abelian group G is a bounded system of compatible measures on the compact quotients of G . We study the Banach algebra of densities on G , using the theory of almost periodic functions as a principal tool. In particular, we characterize those groups G in which each density is induced by a measure on the semi-periodic compactification of G . There are applications to the theory of uniform distribution.

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