Continuation of Conditional Probabilities
Teoriâ veroâtnostej i ee primeneniâ, Tome 6 (1961) no. 1, pp. 116-118
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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.
@article{TVP_1961_6_1_a12,
author = {N. N. Vorob'ev and D. K. Faddeev},
title = {Continuation of {Conditional} {Probabilities}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {116--118},
publisher = {mathdoc},
volume = {6},
number = {1},
year = {1961},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1961_6_1_a12/}
}
N. N. Vorob'ev; D. K. Faddeev. Continuation of Conditional Probabilities. Teoriâ veroâtnostej i ee primeneniâ, Tome 6 (1961) no. 1, pp. 116-118. http://geodesic.mathdoc.fr/item/TVP_1961_6_1_a12/