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On the Brunn-Minkowski coefficient of a locally compact unimodular group

Published online by Cambridge University Press:  24 October 2008

M. McCrudden
M. McCrudden
Affiliation:
Birmingham University
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Extract

Let G be a locally compact topological group, and let μ be the left Haar measure on G, with μ the corresponding outer measure. If R' denotes the non-negative extended real numbers, B (G) the Borel subsets of G, and V = {μ(C):C ∈ B(G)}, then we can define ΦG: V × V → R' by

where AB denotes the product set of A and B in G. Then clearly

so that a knowledge of ΦG will give us some idea of how the outer measure of the product set AB compares with the measures of the sets A and B.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 1 , January 1969 , pp. 33 - 45
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

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