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December, 1973 Limits of Ratios of Tails of Measures
Walter Rudin
Ann. Probab. 1(6): 982-994 (December, 1973). DOI: 10.1214/aop/1176996805


Suppose $\mu$ is a positive measure on the half-line $\lbrack 0, \infty)$, of total mass $m, \Phi$ is the sum of a power series with nonnegative coefficients which converges at the point $m$, and $\lambda$ is the measure on $\lbrack 0, \infty)$ whose Fourier transform $\hat{\lambda}$ is $\Phi(\hat{\mu})$. The lower limit of the ratios $\lambda(\lbrack s, \infty))/\mu(\lbrack s, \infty))$, as $s\rightarrow\infty$, is compared to the number $\Phi'(m)$, under a variety of conditions.


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Walter Rudin. "Limits of Ratios of Tails of Measures." Ann. Probab. 1 (6) 982 - 994, December, 1973.


Published: December, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0303.60014
MathSciNet: MR358919
Digital Object Identifier: 10.1214/aop/1176996805

Primary: 60E05
Secondary: 60F99

Keywords: Convolutions , functions of measures , tails of measures

Rights: Copyright © 1973 Institute of Mathematical Statistics

Vol.1 • No. 6 • December, 1973
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