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The approximation of Gδ-sets, in measure, by Fσ-sets

Published online by Cambridge University Press:  24 October 2008

D. G. Larman
D. G. Larman
Affiliation:
University College, London
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Some time ago Besicovitch(l) gave an example of a linear Gδ-set E of Besicovitch dimension 1, with the property that E – A also has dimension 1, for each Fσ.-set A contained in E. This shows that an Fσ-set contained in E cannot be a very close approximation to E, but it leaves plenty of scope for Fσ-sets contained in E to be reasonably good approximations to E.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 1 , January 1965 , pp. 105 - 107
Copyright
Copyright © Cambridge Philosophical Society 1965

References

REFERENCES

(1)Besicovitch, A. S.On the approximation in measure to Borel sets by F σ-sets. J. London Math. Soc. 29 (1954), 382–383.CrossRefGoogle Scholar
(2)Besicovitch, A. S. and Moran, P. A. P.The measure of product and cylinder sets. J. London Math. Soc. 20 (1945), 110–120.Google Scholar