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On Uniform Asymptotic Upper Density in Locally Compact Abelian Groups by Revesz, Szilard Gy. is a scholarly article available to read on EtoBox.

What is On Uniform Asymptotic Upper Density in Locally Compact Abelian Groups about?

Starting out from results known for the most classical cases of N, Z^d, R^d or for sigma-finite abelian groups, here we define the notion of asymptotic uniform upper density in general locally compact abelian groups. Even if a bit surprising, the new notion proves to be the right extension of the classical cases of Z^d, R^d. The new notion is used to extend some analogous results previously obtained only for classical cases or sigma-finite abelian groups. In particular, we show the following extension of a well-known result for Z of Furstenberg: if in a general locally compact Abelian group G a subset S of G has positive uniform asymptotic upper density, then S-S is syndetic.

Author

Revesz, Szilard Gy.

Published

2009

Language

EN