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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

Leningrad

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

Received: 08.10.1959

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}


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