### Densities on locally compact abelian groups

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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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