Thick Difference Sets of Haar Null Compact Sets in Locally Compact Groups
Abstract
Let \(G\) be a non-discrete, locally compact group with Haar measure \(m\). We prove that there exists a compact set \(K ⊂ G\) 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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