Geodesic
Monotone nonincreasing random fields on posets. II. Probability distributions on polyhedral cones
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part X, Tome 307 (2004), pp. 5-56 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this part of the paper we investigate the structure of an arbitrary measure $\mu$ concentrated on a polyhedral cone $C$ in $\mathbf{R}^d$ in the case when the decumulative distribution function $g_\mu$ of the measure $\mu$ satisfies certain continuity conditions. If a face $\Gamma$ of the cone $C$ satisfies appropriate conditions, the restriction $\mu|_{\Gamma^{\operatorname{int}}}$ of the measure $\mu$ to the inner part of $\Gamma$ is proved to be absolutely continuous with respect to the Lebesgue measure $\lambda_\Gamma$ on the face $\Gamma$. Besides, the density of the measure $\mu|_{\Gamma^{\operatorname{int}}}$ is expressed as a derivative of the function $g_\mu$ multipied by a constant. This result was used in the first part of the paper to find the finite-dimensional distributions of a monotone random field on a poset. 
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     author = {L. B. Beinenson},
     title = {Monotone nonincreasing random fields on posets. {II.~Probability} distributions on polyhedral cones},
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     year = {2004},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_307_a0/}
}
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L. B. Beinenson. Monotone nonincreasing random fields on posets. II. Probability distributions on polyhedral cones. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part X, Tome 307 (2004), pp. 5-56. http://geodesic.mathdoc.fr/item/ZNSL_2004_307_a0/

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