On functional equations associated with characters of unitary representations of groups.
On Haar null sets
We prove that in Polish, abelian, non-locally-compact groups the family of Haar null sets of Christensen does not fulfil the countable chain condition, that is, there exists an uncountable family of pairwise disjoint universally measurable sets which are not Haar null. (Dougherty, answering an old question of Christensen, showed earlier that this was the case for some Polish, abelian, non-locally-compact groups.) Thus we obtain the following characterization of locally compact, abelian groups: Let...
On Hausdorff dimension of random fractals.
On invariant measures for piecewise convex transformations
On Invariant Measures, Minimal Sets and a Lemma of Margulies.
On invariant measures of nonlinear Markov processes.
On Ito-Nisio type theorems for DS-groups.
On measures in fibre spaces
On nonmeasurable selectors of countable group actions
Given a set X, a countable group H acting on it and a σ-finite H-invariant measure m on X, we study conditions which imply that each selector of H-orbits is nonmeasurable with respect to any H-invariant extension of m.
On products of Radon measures
Let with card Γ ≥ c (c denotes the continuum). We construct two Radon measures μ,ν on X such that there exist open subsets of X × X which are not measurable for the simple outer product measure. Moreover, these measures are strikingly similar to the Lebesgue product measure: for every finite F ⊆ Γ, the projections of μ and ν onto are equivalent to the F-dimensional Lebesgue measure. We generalize this construction to any compact group of weight ≥ c, by replacing the Lebesgue product measure...
On the differentiation theorem in metric groups
On the existence of a Haar measure in topological IP-loops
In this paper, we give conditions ensuring the existence of a Haar measure in topological IP-loops.
On the existence of invariant measures for Markov processes
On the generalized Avez method
A generalization of the Avez method of construction of an invariant measure is presented.
On the Property P... of Locally Compact Groups
On the Proportionality of Covolumes of Discrete Subgroups.
On the uniqueness property for products of symmetric invariant probability measures.
On the Variation in the Cohomology of the Symplectic Form of the Reduced Phase Space.
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...
Partial densities on the group of integers
Conditions are obtained under which a partial density on the group of integers with the discrete topology can be extended to a density.