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An Fσ semigroup of zero measure which contains a translate of every countable set
Published online by Cambridge University Press: 26 February 2010
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.
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