On various notions of regularity in ordered spaces
On vector lattice-valued measures. I.
On vector measures
Let be the Banach space of real measures on a -ring , let be its dual, let be a quasi-complete locally convex space, let be its dual, and let be an -valued measure on . If is shown that for any there exists an element of such that for any and that the mapis order continuous. It follows that the closed convex hull of is weakly compact.
On Vector Measures in Cartesian Products
On vector measures which have everywhere infinite variation or noncompact range [Book]
On vector sums of measure zero sets.
On vector-topological properties of zero-neighbourhoods of topological vector spaces
On Vitali-Hahn-Saks-Nikodym type theorems
A Boolean algebra has the interpolation property (property (I)) if given sequences , in with for all , there exists an element in such that for all . Let denote an algebra with the property (I). It is shown that if ( a Banach space) is a sequence of strongly additive measures such that exists for each , then defines a strongly additive map from to and the are uniformly strongly additive. The Vitali-Hahn-Saks (VHS) theorem for strongly additive -valued measures defined...
On Vitali's theorem for groups of motions of Euclidean space.
On Weak Compactness and Lower Closure Results for Pettis Integrable (Multi)Functions
In [4, 5, 7] an abstract, versatile approach was given to sequential weak compactness and lower closure results for scalarly integrable functions and multifunctions. Its main tool is an abstract version of the Komlós theorem, which applies to scalarly integrable functions. Here it is shown that this same approach also applies to Pettis integrable multifunctions, because the abstract Komlós theorem can easily be extended so as to apply to generalized Pettis integrable functions. Some results in the...
On Weak Convergence of Norm Preserving Operators on L2 (X) and its Application to Measure Preserving Transformations.
On Weak Convergence of Stochastic Processes With Lusin Path Spaces.
On weakly* conditionally compact dynamical systems
On weakly convergent nets in spaces of non-negative measures
On Weakly Measurable Functions
We show that if T is an uncountable Polish space, 𝓧 is a metrizable space and f:T→ 𝓧 is a weakly Baire measurable function, then we can find a meagre set M ⊆ T such that f[T∖M] is a separable space. We also give an example showing that "metrizable" cannot be replaced by "normal".
On weakly measurable stochastic processes and absolutely summing operators
A characterization of absolutely summing operators by means of McShane integrable stochastic processes is considered.
On weighted inequalities for ergodic operators
On -invariant measures and a functional equation
On -discrete Borel mappings via quasi-metrics
On -porous sets in abstract spaces.