J Austral Math Soc Ser A 43 pp211--219, 1987.

Coin Tossing and Sum Sets

Gavin Brown and John H. Williamson

Abstract

We consider the distribution of numbers whose binary digits are generated from infinitely many tosses of a biased coin. It is shown that, if E has positive m 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 m are singular.

1980 AMS Subject Classification: primary 60B15; secondary 43A05

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Authors

Gavin Brown

John H. Williamson

Department of Pure Mathematics, University of New South Wales, Kensington, 2033, N.S.W., Australia.