On the existence problem in the algebraic approach to quantum field theory
On the expected value of vector lattice-valued random variables
On the Extension of a Measure on Lattices
On the extension of -poset valued measures
A variant of Alexandrov theorem is proved stating that a compact, subadditive -poset valued mapping is continuous. Then the measure extension theorem is proved for MV-algebra valued measures.
On the extension of measures.
We give necessary and sufficient conditions for a totally ordered by extension family (Ω, Σx, μx)x ∈ X of spaces of probability to have a measure μ which is an extension of all the measures μx. As an application we study when a probability measure on Ω has an extension defined on all the subsets of Ω.
On the extension of measures
On the Extension of Measures in Relatively Complemented Lattices
On the extension of positive operators
On the extension of subadditive measures in lattice ordered groups
A lattice ordered group valued subadditive measure is extended from an algebra of subsets of a set to a -algebra.
On the Extremality of measure extensions.
On the extremality of regular extensions of contents and measures
Let be an algebra and a lattice of subsets of a set . We show that every content on that can be approximated by in the sense of Marczewski has an extremal extension to a -regular content on the algebra generated by and . Under an additional assumption, we can also prove the existence of extremal regular measure extensions.
On the Functional Equation f(x)g(y) = ...hi(aix + biy).
On the -entropy and its Hudetz correction
The Hudetz correction of the fuzzy entropy is applied to the -entropy. The new invariant is expressed by the Hudetz correction of fuzzy entropy.
On the generalization of the Stein-Weiss theorem for the ergodic Hilbert transform
The Stein-Weiss theorem that the distribution function of the Hilbert transform of the characteristic function of E depends only on the measure of E is generalized to the ergodic Hilbert transform.
On the generalized Avez method
A generalization of the Avez method of construction of an invariant measure is presented.
On the generalized continuity of the semivariation in locally convex spaces
On the geometric structure of the limit set of conformal iterated function systems.
On the geometrical structure of Lebesgue nullsets
On the growth of averaged Weyl sums for rigid rotations
On the Hausdorff dimension of a family of self-similar sets with complicated overlaps
We investigate the properties of the Hausdorff dimension of the attractor of the iterated function system (IFS) {γx,λx,λx+1}. Since two maps have the same fixed point, there are very complicated overlaps, and it is not possible to directly apply known techniques. We give a formula for the Hausdorff dimension of the attractor for Lebesgue almost all parameters (γ,λ), γ < λ. This result only holds for almost all parameters: we find a dense set of parameters (γ,λ) for which the Hausdorff dimension...