A Perron-type integral of order for Riesz spaces
On Stone-type extensions for group-valued measures
Uniform (s)-boundedness and regularity for (l)-group-valued measures
Some new results about uniform (s)-boundedness for regular (l)-group-valued set functions are given.
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.
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...
Some new results about Brooks-Jewett and Dieudonné-type theorems in -groups
In this paper we present some new versions of Brooks-Jewett and Dieudonné-type theorems for -group-valued measures.
A skeleton of Fubini-type theorem in vector spaces for the Kurzweil integral and operator measures
Dieudonné-type theorems for lattice group-valued -triangular set functions
Some versions of Dieudonné-type convergence and uniform boundedness theorems are proved, for -triangular and regular lattice group-valued set functions. We use sliding hump techniques and direct methods. We extend earlier results, proved in the real case. Furthermore, we pose some open problems.
Some versions of limit and Dieudonné-type theorems with respect to filter convergence for (ℓ)-group-valued measures
Some limit and Dieudonné-type theorems in the setting of (ℓ)-groups with respect to filter convergence are proved, extending earlier results.
Ideal convergence and divergence of nets in -groups
In this paper we introduce the - and -convergence and divergence of nets in -groups. We prove some theorems relating different types of convergence/divergence for nets in -group setting, in relation with ideals. We consider both order and -convergence. By using basic properties of order sequences, some fundamental properties, Cauchy-type characterizations and comparison results are derived. We prove that -convergence/divergence implies -convergence/divergence for every ideal, admissible for...
Abstract Korovkin-type theorems in modular spaces and applications
We prove some versions of abstract Korovkin-type theorems in modular function spaces, with respect to filter convergence for linear positive operators, by considering several kinds of test functions. We give some results with respect to an axiomatic convergence, including almost convergence. An extension to non positive operators is also studied. Finally, we give some examples and applications to moment and bivariate Kantorovich-type operators, showing that our results are proper extensions of the...
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