The Annals of Probability

There are no Borel SPLIFs

D. Blackwell

Full-text: Open access

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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 28A20: Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
Secondary: 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]

Keywords
Convergence in probability Borel function

Citation

Blackwell, D. There are no Borel SPLIFs. Ann. Probab. 8 (1980), no. 6, 1189--1190. doi:10.1214/aop/1176994581. https://projecteuclid.org/euclid.aop/1176994581


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