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A measure which is singular and uniformly locally uniform

Authors: David Freedman and Jim Pitman
Journal: Proc. Amer. Math. Soc. 108 (1990), 371-381
MSC: Primary 28A12; Secondary 62F12, 62F15
MathSciNet review: 990427
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Abstract: An example is given of a singular measure on $ [0,1]$ which is locally nearly uniform in the weak star topology. If this measure is used as a prior to estimate an unknown probability in coin tossing, the posterior is asymptotically normal.

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Keywords: Differentiation, Lebesgue points, Bayes estimates, Riesz product, singular measure, locally uniform measure, asymptotic normality of posterior distribution
Article copyright: © Copyright 1990 American Mathematical Society

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