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It is a well-known fact that the Dempster combination rule for combination of uncertainty degrees coming from two or more sources is legitimate only if the combined empirical data, charged with uncertainty and taken as random variables, are statistically (stochastically) independent. We shall prove, however, that for a particular but large enough class of probability measures, an analogy of Dempster combination rule, preserving its extensional character but using some nonstandard and boolean-like...

A note on nonaxiomatizability of independence relations generated by certain probabilistic structures

Ivan Kramosil (1988)

Kybernetika

A Note on Quasicontinuous Kernels Representing Quasi-Linear Positive Maps.

Sergio Albeverio, Zhi-Ming Ma (1991)

Forum mathematicum

A note on strong laws of large numbers for dependent random sets and fuzzy random sets.

Fu, Ke-Ang (2010)

Journal of Inequalities and Applications [electronic only]

A note on the interval-valued marginal problem and its maximum entropy solution

Jiřina Vejnarová (1998)

Kybernetika

This contribution introduces the marginal problem, where marginals are not given precisely, but belong to some convex sets given by systems of intervals. Conditions, under which the maximum entropy solution of this problem can be obtained via classical methods using maximum entropy representatives of these convex sets, are presented. Two counterexamples illustrate the fact, that this property is not generally satisfied. Some ideas of an alternative approach are presented at the end of the paper.

A probabilistic ergodic decomposition result

Albert Raugi (2009)

Annales de l'I.H.P. Probabilités et statistiques

Let $(X, 𝔛, μ)$ be a standard probability space. We say that a sub-σ-algebra $𝔅$ of $𝔛$ decomposes μ in an ergodic way if any regular conditional probability $^{𝔅} P$ with respect to $𝔅$ andμ satisfies, for μ-almost every x∈X, $\forall B \in 𝔅,^{𝔅} P (x, B) \in {0, 1}$ . In this case the equality $μ (\cdot) = \int_{X}^{𝔅} P (x, \cdot) μ (d x)$ , gives us an integral decomposition in “ $𝔅$ -ergodic” components. For any sub-σ-algebra $𝔅$ of $𝔛$ , we denote by $\bar{𝔅}$ the smallest sub-σ-algebra of $𝔛$ containing $𝔅$ and the collection of all setsAin $𝔛$ satisfyingμ(A)=0. We say that $𝔅$ isμ-complete if $𝔅 = \bar{𝔅}$ . Let ${𝔅_{i} i \in I}$ be a non-empty family...

A property of doubly stochastic densities

Anzelm Iwanik (1989)

Acta Universitatis Carolinae. Mathematica et Physica

A remark on metrics for finitely additive distribution functions.

Silvano Holzer, Carlo Sempi (1986)

Stochastica

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