On the lattice group valued submeasures
On the Law of Large Numbers for Nonmeasurable Identically Distributed Random Variables
Let Ω be a countable infinite product of copies of the same probability space Ω₁, and let Ξₙ be the sequence of the coordinate projection functions from Ω to Ω₁. Let Ψ be a possibly nonmeasurable function from Ω₁ to ℝ, and let Xₙ(ω) = Ψ(Ξₙ(ω)). Then we can think of Xₙ as a sequence of independent but possibly nonmeasurable random variables on Ω. Let Sₙ = X₁ + ⋯ + Xₙ. By the ordinary Strong Law of Large Numbers, we almost surely have , where and E* are the lower and upper expectations. We ask...
On the Minimal Convex Annulus of a Planar Convex Body.
On the uniqueness of Lebesgue and Borel measures.
On the Ward Theorem for -adic-path bases associated with a bounded sequence
In this paper we prove that each differentiation basis associated with a -adic path system defined by a bounded sequence satisfies the Ward Theorem.
On trigonometric polynomials spanned by characters of unitary representations.
On two strengthenings of regularity of measures
On uncountable unions and intersections of measurable sets.
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-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 .
Outer measure analysis of topological lattice properties.
Outer measures and associated lattice properties.
Outer measures associated with lattice measures and their application.
Outer measures, measurability, and lattice regular measures.
-symmetric bi-capacities
Bi-capacities have been recently introduced as a natural generalization of capacities (or fuzzy measures) when the underlying scale is bipolar. They allow to build more flexible models in decision making, although their complexity is of order , instead of for fuzzy measures. In order to reduce the complexity, the paper proposes the notion of -symmetric bi- capacities, in the same spirit as for -symmetric fuzzy measures. The main idea is to partition the set of criteria (or states of nature,...
Packing measures on Euclidean spaces
Packing measures on ultrametric spaces
Partial measures.
Pathological Linear Spaces and Submeasures.