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December, 1980 There are no Borel SPLIFs
D. Blackwell
Ann. Probab. 8(6): 1189-1190 (December, 1980). DOI: 10.1214/aop/1176994581


There is no Borel function $f$, defined for all infinite sequences of 0's and 1's, such that for every sequence $X$ of 0-1 random variables that converges in probability to a constant $c$, we have $f(x) = c$ a.s.


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D. Blackwell. "There are no Borel SPLIFs." Ann. Probab. 8 (6) 1189 - 1190, December, 1980.


Published: December, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0451.28001
MathSciNet: MR602393
Digital Object Identifier: 10.1214/aop/1176994581

Primary: 28A20
Secondary: 28A05

Keywords: Borel function , convergence in probability

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 6 • December, 1980
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