There are no Borel SPLIFs

D. Blackwell

doi:10.1214/aop/1176994581

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Home > Journals > Ann. Probab. > Volume 8 > Issue 6 > Article

December, 1980 There are no Borel SPLIFs

D. Blackwell

Ann. Probab. 8(6): 1189-1190 (December, 1980). DOI: 10.1214/aop/1176994581

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Abstract

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.