Szemeredi-type theorems for subsets of locally compact abelian groups of positive upper Banach density


By using ergodic theoretic techniques following Hillel F\"{u}rstenberg, we prove that measurable subsets of a locally compact abelian group of positive upper density contain Szemer\'{e}di-wise configurations defined by an arbitrary compact subset of the group.Comment: 11 pages; accepted by Acta Arit

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