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An Fσ semigroup of zero measure which contains a translate of every countable set

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

J. A. Haight
J. A. Haight
Affiliation:
Department of Mathematics, University College London, Gower Street, London. WC1E 6BT
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Extract

In 1942 Piccard [10] gave an example of a set of real numbers whose sum set has zero Lebesgue measure but whose difference set contains an interval. About thirty years later various authors (Connolly, Jackson, Williamson and Woodall) in a series of papers constructed F σ sets E in ℝ such that E – E contains an interval while the K-fold sum set

has zero Lebesgue measure for progressively larger values of k.

MSC classification

Secondary: 28A75: Length, area, volume, other geometric measure theory
Type
Research Article
Information
Mathematika , Volume 31 , Issue 2 , December 1984 , pp. 272 - 281
Copyright
Copyright © University College London 1984

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References

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