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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1961, Volume 6, Issue 1, Pages 116–118 (Mi tvp4757)

Short Communications

Continuation of Conditional Probabilities

N. N. Vorob'ev, D. K. Faddeev

Abstract: A probability measure $\mu$ on a finite set $R$ is called interior if $\mu(a)>0$ for any $a\in R$. The set of all interior measures on $R$ is denoted by $W(R)$.
Theorem. There exists a mapping $\varphi$ of $W(R)$ into Euclidean space $E$ of suitable dimension with two properties:
1. All conditional probabilities
$$\mu(a|A)=\frac{\mu (a)}{\mu (A)},\quad a\in A\subset R,$$
are uniformly continuous functions $\varphi(\mu)$ on the whole set $\varphi W(R)$ in the sense of the metric on $E$.
2. The closure of $\varphi W(R)$ in $E$ is homeomorphic to the closed simplex of suitable dimension.

Full text: PDF file (315 kB)

English version:
Theory of Probability and its Applications, 1961, 6:1, 105–107

Citation: N. N. Vorob'ev, D. K. Faddeev, “Continuation of Conditional Probabilities”, Teor. Veroyatnost. i Primenen., 6:1 (1961), 116–118; Theory Probab. Appl., 6:1 (1961), 105–107

Citation in format AMSBIB
\Bibitem{VorFad61} \by N.~N.~Vorob'ev, D.~K.~Faddeev \paper Continuation of Conditional Probabilities \jour Teor. Veroyatnost. i Primenen. \yr 1961 \vol 6 \issue 1 \pages 116--118 \mathnet{http://mi.mathnet.ru/tvp4757} \transl \jour Theory Probab. Appl. \yr 1961 \vol 6 \issue 1 \pages 105--107 \crossref{https://doi.org/10.1137/1106013}