Geodesic
Two dimensional probabilities with a given conditional structure
Kybernetika, Tome 35 (1999) no. 3, pp. 367-381 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A properly measurable set ${\cal P} \subset {X} \times M_1({Y})$ (where ${X}, {Y}$ are Polish spaces and $M_1(Y)$ is the space of Borel probability measures on $Y$) is considered. Given a probability distribution $\lambda \in M_1(X)$ the paper treats the problem of the existence of ${X}\times {Y}$-valued random vector $(\xi ,\eta )$ for which ${\cal L}(\xi )=\lambda $ and ${\cal L}(\eta | \xi =x) \in {\cal P}_x$ $\lambda $-almost surely that possesses moreover some other properties such as “${\cal L}(\xi ,\eta )$ has the maximal possible support” or “${\cal L}(\eta | \xi =x)$’s are extremal measures in ${\cal P}_x$’s”. The paper continues the research started in [7].
A properly measurable set ${\cal P} \subset {X} \times M_1({Y})$ (where ${X}, {Y}$ are Polish spaces and $M_1(Y)$ is the space of Borel probability measures on $Y$) is considered. Given a probability distribution $\lambda \in M_1(X)$ the paper treats the problem of the existence of ${X}\times {Y}$-valued random vector $(\xi ,\eta )$ for which ${\cal L}(\xi )=\lambda $ and ${\cal L}(\eta | \xi =x) \in {\cal P}_x$ $\lambda $-almost surely that possesses moreover some other properties such as “${\cal L}(\xi ,\eta )$ has the maximal possible support” or “${\cal L}(\eta | \xi =x)$’s are extremal measures in ${\cal P}_x$’s”. The paper continues the research started in [7].
Classification : 28A35, 60A10, 60B05, 60E05
Keywords: two-dimensional probabilities; extremal measure 
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     title = {Two dimensional probabilities with a given conditional structure},
     journal = {Kybernetika},
     pages = {367--381},
     year = {1999},
     volume = {35},
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     zbl = {1274.60014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1999_35_3_a5/}
}
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Štěpán, Josef; Hlubinka, Daniel. Two dimensional probabilities with a given conditional structure. Kybernetika, Tome 35 (1999) no. 3, pp. 367-381. http://geodesic.mathdoc.fr/item/KYB_1999_35_3_a5/

[1] Aubin J.-P., Frankowska H.: Set Valued Analysis. Birkhäuser, Boston 1990 | MR | Zbl

[2] Beneš V., (eds.) J. Štěpán: Distributions with Given Marginals and Moment Problems. Kluwer, Dordrecht 1997 | MR | Zbl

[3] Cohn D. L.: Measure Theory. Birkhäuser, Boston 1980 | MR | Zbl

[4] Kempermann J. H. B.: The general moment problem, a geometric approach. Ann. Math. Statist. 39 (1968), 93–122 | DOI | MR

[5] Meyer P. A.: Probability and Potentials. Blaisdell, Waltham 1966 | MR | Zbl

[6] Schwarz L.: Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures. Oxford University Press, Oxford 1973 | MR

[8] Winkler G.: Choquet Order and Simplices. (Lectures Notes in Mathematics 1145.) Springer–Verlag, Berlin 1985 | MR | Zbl