Translator Disclaimer
December, 1979 Conditional Distributions as Derivatives
P. Pfanzagl
Ann. Probab. 7(6): 1046-1050 (December, 1979). DOI: 10.1214/aop/1176994897

Abstract

Let $(X, \mathscr{a}, P)$ be a probability space, $Y$ a complete separable metric space, $Z$ a separable metric space, and $s: X\rightarrow Y, t: X\rightarrow Z$ Borel measurable functions. Then the weak limit of $P\{s \in B, t \in C\}/P\{t \in C\}$ for $C\downarrow\{z\}$ exists for $P-\mathrm{a.a.} z \in Z$, and is a regular conditional distribution of $s$, given $t$.

Citation

Download Citation

P. Pfanzagl. "Conditional Distributions as Derivatives." Ann. Probab. 7 (6) 1046 - 1050, December, 1979. https://doi.org/10.1214/aop/1176994897

Information

Published: December, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0427.60003
MathSciNet: MR548898
Digital Object Identifier: 10.1214/aop/1176994897

Subjects:
Primary: 60A10
Secondary: ‎28A15

Rights: Copyright © 1979 Institute of Mathematical Statistics

JOURNAL ARTICLE
5 PAGES


SHARE
Vol.7 • No. 6 • December, 1979
Back to Top