Densities on locally compact abelian groups
Annales de l'Institut Fourier, Volume 19 (1969) no. 1, pp. 81-107.

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.

Une densité sur un groupe abélien localement compact G est un système borné de mesures cohérentes sur les quotients compacts de G. Nous étudions l’algèbre de Banach des densités sur G, en utilisant la théorie des fonctions presque périodiques comme moyen d’investigation principal. En particulier, nous caractérisons les groupes G dans lesquels chaque densité est induite par une mesure sur le compactifié semi-périodique de G. On donne des applications à la théorie d’équirépartition.

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     title = {Densities on locally compact abelian groups},
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     pages = {81--107},
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     volume = {19},
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     year = {1969},
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Berg, I. D.; Rubel, L. A. Densities on locally compact abelian groups. Annales de l'Institut Fourier, Volume 19 (1969) no. 1, pp. 81-107. doi : 10.5802/aif.308. http://www.numdam.org/articles/10.5802/aif.308/

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[7] W. Rudin, Fourier Analysis in Groups, Interscience Publishers, (1962), New-York. | MR | Zbl

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