On regular and sigma-smooth two valued measures and lattice generated topologies.
On some properties of submeasures on MV-algebras
On the classification of Markov chains via occupation measures
We consider a Markov chain on a locally compact separable metric space and with a unique invariant probability. We show that such a chain can be classified into two categories according to the type of convergence of the expected occupation measures. Several properties in each category are investigated.
On the complexity of sums of Dirichlet measures
Let be the set of all Dirichlet measures on the unit circle. We prove that is a non Borel analytic set for the weak* topology and that is not norm-closed. More precisely, we prove that there is no weak* Borel set which separates from (or even , the set of all measures singular with respect to every measure in . This extends results of Kaufman, Kechris and Lyons about and and gives many examples of non Borel analytic sets.
On the Extremality of measure extensions.
On the setwise convergence of sequences of measures.
On the Urysohn condition and the convergence of probability distributions
On Ulam's problem on families of measures
On uniform tail expansions of multivariate copulas and wide convergence of measures
The theory of copulas provides a useful tool for modeling dependence in risk management. In insurance and finance, as well as in other applications, dependence of extreme events is particularly important, hence there is a need for a detailed study of the tail behaviour of multivariate copulas. We investigate the class of copulas having regular tails with a uniform expansion. We present several equivalent characterizations of uniform tail expansions. Next, basing on them, we determine the class of...
On weakly convergent nets in spaces of non-negative measures
On -porous sets in abstract spaces.
Open mapping theorems for capacities
For the functor of upper semicontinuous capacities in the category of compact Hausdorff spaces and two of its subfunctors, we prove open mapping theorems. These are counterparts of the open mapping theorem for the probability measure functor proved by Ditor and Eifler.
Order boundedness and weak compactness of the set of quasi-measure extensions of a quasi-measure
Let and be algebras of subsets of a set with , and denote by the set of all quasi-measure extensions of a given quasi-measure on to . We give some criteria for order boundedness of in , in the general case as well as for atomic . Order boundedness implies weak compactness of . We show that the converse implication holds under some assumptions on , and or alone, but not in general.
Order Conditioned Indepencence of Real Random Variables.
Order convergence of vector measures on topological spaces
Let be a completely regular Hausdorff space, a boundedly complete vector lattice, the space of all, bounded, real-valued continuous functions on , the algebra generated by the zero-sets of , and a positive linear map. First we give a new proof that extends to a unique, finitely additive measure such that is inner regular by zero-sets and outer regular by cozero sets. Then some order-convergence theorems about nets of -valued finitely additive measures on are proved, which extend...
Order-theoretic properties of some sets of quasi-measures
Let and be algebras of subsets of a set with , and denote by the set of all quasi-measure extensions of a given quasi-measure on to . We show that is order bounded if and only if it is contained in a principal ideal in if and only if it is weakly compact and is contained in a principal ideal in . We also establish some criteria for the coincidence of the ideals, in , generated by and .
Poissonian products of random weights: uniform convergence and related measures.
Properties of a special class of doubly stochastic measures.
Proprites de Radon-Nikodym pour les cones positifs de mesures.
Radon-Nikodym theorem in spaces of measures.