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The size of sums of sets. (English) Zbl 0615.43001

Lower bounds are obtained for the Haar measure of the set \(K+E\) when K and E are suitable subsets of a locally compact abelian group. An example is the following inequality \[ m(K-K) m(E)\leq [m(K+E)]^ 2. \]

MSC:

43A05 Measures on groups and semigroups, etc.
22B99 Locally compact abelian groups (LCA groups)
28C10 Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
11B05 Density, gaps, topology
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