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Teoriya Veroyatnostei i ee Primeneniya, 1961, Volume 6, Issue 1, Pages 116–118
(Mi tvp4757)
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This article is cited in 1 scientific paper (total in 1 paper)
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.
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
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