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

## TL;DR

This paper extends Szemerédi-type theorems to measurable subsets of locally compact abelian groups with positive upper density, demonstrating they contain complex configurations defined by any compact subset, using ergodic theory techniques.

## Contribution

It introduces a new ergodic theoretic approach to establish Szemerédi-type results in the setting of locally compact abelian groups with positive density.

## Key findings

- Measurable subsets of locally compact abelian groups with positive density contain Szemerédi configurations.
- The results generalize classical Szemerédi theorems to a broader algebraic setting.
- Ergodic methods effectively prove combinatorial properties in topological group contexts.

## Abstract

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.