The Kluvanek-Kantorovitz characterization of scalar operators in locally convex spaces.
The Kurzweil construction of an integral in ordered spaces
This paper generalizes the results of papers which deal with the Kurzweil-Henstock construction of an integral in ordered spaces. The definition is given and some limit theorems for the integral of ordered group valued functions defined on a Hausdorff compact topological space with respect to an ordered group valued measure are proved in this paper.
The Laplace transform of exponentially bounded vector-valued functions (real conditions)
The McShane, PU and Henstock integrals of Banach valued functions
Some relationships between the vector valued Henstock and McShane integrals are investigated. An integral for vector valued functions, defined by means of partitions of the unity (the PU-integral) is studied. In particular it is shown that a vector valued function is McShane integrable if and only if it is both Pettis and PU-integrable. Convergence theorems for the Henstock variational and the PU integrals are stated. The families of multipliers for the Henstock and the Henstock variational integrals...
The monotone convergence theorem for multidimensional abstract Kurzweil vector integrals
We prove two versions of the Monotone Convergence Theorem for the vector integral of Kurzweil, , where is a compact interval of , and are functions with values on and respectively, and and are monotone ordered normed spaces. Analogous results can be obtained for the Kurzweil vector integral, , as well as to unbounded intervals .
The monotone limit convergence theorem for elementary functions with values in a vector lattice
The multiplier for the weak McShane integral
The multiplier for the weak McShane integral which has been introduced by M. Saadoune and R. Sayyad (2014) is characterized.
The Nikodym theorems for operator measures.
The optional sampling theorem for convex set valued martingales.
The Perron product integral in Lie groups
The Radon-Nikodym property and convergence of amarts in Frechet spaces
The range of vector measures into Orlicz spaces
The reciprocal Dunford–Pettis property of order in projective tensor products
We investigate whether the projective tensor product of two Banach spaces and has the reciprocal Dunford–Pettis property of order , , when and have the respective property.
The regular component of a group-valued set function
The s-Perron, sap-Perron and ap-McShane integrals
In this paper, we study the s-Perron, sap-Perron and ap-McShane integrals. In particular, we show that the s-Perron integral is equivalent to the McShane integral and that the sap-Perron integral is equivalent to the ap-McShane integral.
The symmetric Choquet integral with respect to Riesz-space-valued capacities
A definition of “Šipoš integral” is given, similarly to [3],[5],[10], for real-valued functions and with respect to Dedekind complete Riesz-space-valued “capacities”. A comparison of Choquet and Šipoš-type integrals is given, and some fundamental properties and some convergence theorems for the Šipoš integral are proved.
The theory of stationary vector-valued measures over R.
The Vitali convergence theorem for the vector-valued McShane integral
The classical Vitali convergence theorem gives necessary and sufficient conditions for norm convergence in the space of Lebesgue integrable functions. Although there are versions of the Vitali convergence theorem for the vector valued McShane and Pettis integrals given by Fremlin and Mendoza, these results do not involve norm convergence in the respective spaces. There is a version of the Vitali convergence theorem for scalar valued functions defined on compact intervals in given by Kurzweil and...
The weak McShane integral
We present a weaker version of the Fremlin generalized McShane integral (1995) for functions defined on a -finite outer regular quasi Radon measure space into a Banach space and study its relation with the Pettis integral. In accordance with this new method of integration, the resulting integral can be expressed as a limit of McShane sums with respect to the weak topology. It is shown that a function from into is weakly McShane integrable on each measurable subset of if and only if...
The weak Radon-Nikodym property in Banach spaces