Annular functions in probability
Russell W. Howell
Proc. Amer. Math. Soc. 52 (1975), 217-221
Primary 30A10; Secondary 60G50
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Abstract: A function holomorphic in the open unit disk is said to be strongly annular if there exists a sequence of concentric circles converging outward to the boundary of such that the minimum of on tends to infinity as increases. We show here that such functions with Maclaurin coefficients form a residual set in the space of functions with coefficients . We also show that the set of in for which is strongly annular ( is the th Rademacher function) is residual, and measurable with measure either 0 or .
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