Antonio Boccuto - Academia.edu (original) (raw)

Papers by Antonio Boccuto

summary:In this paper we present some new versions of Brooks-Jewett and Dieudonné-type theorems f... more summary:In this paper we present some new versions of Brooks-Jewett and Dieudonné-type theorems for (l)(l)(l)-group-valued measures

We introduce the GHk integral for functions defined on (possibly) unbounded subintervals of the e... more We introduce the GHk integral for functions defined on (possibly) unbounded subintervals of the extended real line and with values in metric semigroups. Basic properties and convergence theorems for this integral are deduced. AMS (MOS) Subject Classification: 28B15, 46G10.

Real Analysis Exchange, 2008

We find a decomposition of the type of Sobczyk-Hammer for measures with values in l-groups, and a... more We find a decomposition of the type of Sobczyk-Hammer for measures with values in l-groups, and also deduce some convergence theorems for such decompositions. Our procedure is based on some theorems of the type of Vitali-Hahn-Saks, and on the so-called Stone extension method.

Real Analysis Exchange, 2003

Real Analysis Exchange, 2012

Absolute continuity, singularity and Lebesgue decompositions are studied, in the context of the s... more Absolute continuity, singularity and Lebesgue decompositions are studied, in the context of the so-called RD-convergence, for finitely and/or σ− additive measures taking values in super-Dedekind complete l-groups. By means of a Vitali-Hahn-Saks-Nikodm result, found in [4], we deduce a convergence theorem for the Lebesgue decompositions of an RD-convergent sequence of finitely additive measures.

This paper develops an integral and differential calculus for functions with domain and range in ... more This paper develops an integral and differential calculus for functions with domain and range in Dedekind complete Riesz spaces, linked by a ‘product’, taking its values in a third Dedekind complete Rieszs space, where the integrals to be defined assume their values. This product is distributive, compatible with the order of the Riesz spaces, and respects families continuous at zero of arbitrary order. It allows to carry over the concepts of Riemann integrability, uniform continuity, and uniform differentiabilty in a simple way to functions from one Riesz space into another one, retaining the familiar properties of Riemann integrability, like the fundamental theorem of calculus, the exchangeabilty of the integral with the limit for uniformly convergent sequences of functions, and of the derivative with the limit of uniformly differentiable sequences of functions. More important, on this basis a Taylor formula can be deduced by expressing the remainder term by means of the introduced...

Rendiconti del Circolo Matematico di Palermo, 2000

Mathematica Slovaca, 2009

A definition of concave integral is given for real-valued maps and with respect to Dedekind compl... more A definition of concave integral is given for real-valued maps and with respect to Dedekind complete Riesz space-valued “capacities”. Some comparison results with other integrals are given and some convergence theorems are proved.

Information Sciences, 2009

A convergence in Riesz spaces is given axiomatically. A Bochner-type integral for Riesz space-val... more A convergence in Riesz spaces is given axiomatically. A Bochner-type integral for Riesz space-valued functions is introduced and some Vitali and Lebesgue dominated convergence theorems are proved. Some properties and examples are investigated.

Czechoslovak Mathematical Journal, 2008

A definition of "Šipoš integral" is given, similarly as in [3, 5, 10], for real-valued functions ... more A definition of "Šipoš integral" is given, similarly as in [3, 5, 10], for real-valued functions and with respect to Dedekind complete Riesz space-valued "capacities". A comparison between Choquet andŠipoš-type integral is given, and some fundamental properties and some convergence theorems for theŠipoš integral are proved.

Czechoslovak Mathematical Journal, 2004

In this paper we introduce and investigate a Henstock-Kurzweil-type integral for Riesz-space-valu... more 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 which the fact that our integral contains 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 the usual one.

Real Analysis Exchange, 1995

Results in Mathematics

A “Bochner-type” integral for vector lattice-valued functions with respect to (possibly infinite)... more A “Bochner-type” integral for vector lattice-valued functions with respect to (possibly infinite) vector lattice-valued measures is presented with respect to abstract convergences, satisfying suitable axioms, and some fundamental properties are studied. Moreover, by means of this integral, some convergence results on operators in vector lattice-valued modulars are proved. Some applications are given to moment kernels and to the Brownian motion.

arXiv (Cornell University), Oct 31, 2011

A multivalued integral in Riesz spaces is given using the Kurzweil-Henstock integral construction... more A multivalued integral in Riesz spaces is given using the Kurzweil-Henstock integral construction. Some of its properties and a comparison with the Aumann approach are also investigated.

Mathematics, 2020

We introduce Kuelbs–Steadman-type spaces ( K S p spaces) for real-valued functions, with respect ... more We introduce Kuelbs–Steadman-type spaces ( K S p spaces) for real-valued functions, with respect to countably additive measures, taking values in Banach spaces. We investigate the main properties and embeddings of L q -type spaces into K S p spaces, considering both the norm associated with the norm convergence of the involved integrals and that related to the weak convergence of the integrals.

Kybernetika, 2019

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Mathematica Slovaca, 2017

Lp spaces are investigated for vector lattice-valued functions, with respect to filter convergenc... more Lp spaces are investigated for vector lattice-valued functions, with respect to filter convergence. As applications, some classical inequalities are extended to the vector lattice context, and some properties of the Brownian motion and the Brownian bridge are studied, to solve some stochastic differential equations.