## The Annals of Probability

### There are no Borel SPLIFs

D. Blackwell

#### 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.

#### Article information

Source
Ann. Probab., Volume 8, Number 6 (1980), 1189-1190.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176994581

Digital Object Identifier
doi:10.1214/aop/1176994581

Mathematical Reviews number (MathSciNet)
MR602393

Zentralblatt MATH identifier
0451.28001

JSTOR