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A characterization of certain compact sets of measure zero

Published online by Cambridge University Press:  24 October 2008

D. M. Connolly  and
J. H. Williamson
D. M. Connolly
Affiliation:
University of Lethbridge, Alberta, Canada and University of York, England
J. H. Williamson
Affiliation:
University of Lethbridge, Alberta, Canada and University of York, England
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Abstract

We show that the only compact subsets of [0, 1] of measure zero are the obvious ones, and extend this idea to show that the only compact subsets of [0, 1] that generate semigroups of ℝ of measure zero are the obvious ones. We apply this last result to prove that any proper Raikov system of subsets of ℝ, with a single generator, is contained in a strictly larger proper Raikov system.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 2 , September 1975 , pp. 317 - 319
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

(1)Connolly, D. M. and Williamson, J. H.Difference-covers that are not k-sum-covers II. Proc. Cambridge Philos. Soc. 75 (1974), 63–73.CrossRefGoogle Scholar
(2)Williamson, J. H. Raikov systems. Symposia on Theoretical Physics and Mathematics 8, ed. Ramakrishnan, Alladi (New York, 1968).Google Scholar
(3)Williamson, J. H.Raikov systems and the pathology of M(R). Studia Math. 31 (1968), 399–409.CrossRefGoogle Scholar