On the expected value of vector lattice-valued random variables
On the extension of measures
On the generalized continuity of the semivariation in locally convex spaces
On the Henstock-Kurzweil integral for Riesz-space-valued functions defined on unbounded intervals
In this paper we introduce and investigate a Henstock-Kurzweil-type integral for Riesz-space-valued functions defined on (not necessarily bounded) subintervals of the extended real line. We prove some basic properties, among them the fact that our integral contains under suitable hypothesis the generalized Riemann integral and that every simple function which vanishes outside of a set of finite Lebesgue measure is integrable according to our definition, and in this case our integral coincides with...
On the Integration of Radon Measures and Set Functions.
On the product of operator valued measures
On the Product of Vector Measures with Values in Semiordered Spaces
On the space of vector-valued functions integrable with respect to the white noise
On the strong McShane integral of functions with values in a Banach space
The classical Bochner integral is compared with the McShane concept of integration based on Riemann type integral sums. It turns out that the Bochner integrable functions form a proper subclass of the set of functions which are McShane integrable provided the Banach space to which the values of functions belong is infinite-dimensional. The Bochner integrable functions are characterized by using gauge techniques. The situation is different in the case of finite-dimensional valued vector functions....
On the structure of a vector measure.
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 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 weakly measurable stochastic processes and absolutely summing operators
A characterization of absolutely summing operators by means of McShane integrable stochastic processes is considered.
Operator ideal properties of vector measures with finite variation
Given a vector measure m with values in a Banach space X, a desirable property (when available) of the associated Banach function space L¹(m) of all m-integrable functions is that L¹(m) = L¹(|m|), where |m| is the [0,∞]-valued variation measure of m. Closely connected to m is its X-valued integration map Iₘ: f ↦ ∫f dm for f ∈ L¹(m). Many traditional operators from analysis arise as integration maps in this way. A detailed study is made of the connection between the property L¹(m) = L¹(|m|) and the...
Operators from C*-algebras to Banach Spaces.
Operator-Valued Positive Definite Kernels on Tubes.