Thick Difference Sets of Haar Null Compact Sets in Locally Compact Groups

Chuck Akemann

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arXiv · 2603.27479

Thick Difference Sets of Haar Null Compact Sets in Locally Compact Groups

Chuck Akemann

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Abstract

Let $G$ be a non-discrete, locally compact group with Haar measure $m$. We prove that there exists a compact set $K \subset G$ with $m(K)=0$ such that $KK^{-1}$ contains a neighborhood of the identity. Moreover, such a set may be constructed inside any prescribed neighborhood of the identity.

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Chuck Akemann. 2026-03-29. Thick Difference Sets of Haar Null Compact Sets in Locally Compact Groups. https://arxiv.org/abs/2603.27479

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