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Coin tossing and sum sets

Published online by Cambridge University Press:  09 April 2009

Gavin Brown
Affiliation:
Department of Pure MathematicsUniversity of New South WalesKensington, 2033, N.S.W., Australia
John H. Williamson
Affiliation:
Department of Pure MathematicsUniversity of New South WalesKensington, 2033, N.S.W., Australia
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Abstract

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We consider the distribution μ of numbers whose binary digits are generated from infinitely many tosses of a biased coin. It is shown that, if E has positive μ measure, then some n-fold sum of E with itself must contain an interval. This contrasts with the known result that all convolution powers of μ are singular.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1987

References

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