Search results for "28B05"
showing 10 items of 14 documents
Convergence for varying measures
2023
Some limit theorems of the type $\int_{\Omega}f_n dm_n -- --> \int_{\Omega}f dm$ are presented for scalar, (vector), (multi)-valued sequences of m_n-integrable functions f_n. The convergences obtained, in the vector and multivalued settings, are in the weak or in the strong sense.
Non absolutely convergent integrals of functions taking values in a locally convex space
2006
Properties of McShane and Kurzweil-Henstock integrable functions taking values in a locally convex space are considered and the relations with other integrals are studied. A convergence theorem for the Kurzweil-Henstock integral is given
Multi-integrals of finite variation
2020
The aim of this paper is to investigate different types of multi-integrals of finite variation and to obtain decomposition results.
Lineability of non-differentiable Pettis primitives
2014
Let \(X\) be an infinite-dimensional Banach space. In 1995, settling a long outstanding problem of Pettis, Dilworth and Girardi constructed an \(X\)-valued Pettis integrable function on \([0,1]\) whose primitive is nowhere weakly differentiable. Using their technique and some new ideas we show that \(\mathbf{ND}\), the set of strongly measurable Pettis integrable functions with nowhere weakly differentiable primitives, is lineable, i.e., there is an infinite dimensional vector space whose nonzero vectors belong to \(\mathbf{ND}\).
Convergence for varying measures in the topological case
2023
In this paper convergence theorems for sequences of scalar, vector and multivalued Pettis integrable functions on a topological measure space are proved for varying measures vaguely convergent.
The Variational Mcshane Integral in Locally Convex Spaces
2009
The variational McShane integral for functions taking values in a locally convex space is defined, and it is characterized by means of the p-variation of the indefinite Pettis integral
Differentiation of an additive interval measure with values in a conjugate Banach space
2014
We present a complete characterization of finitely additive interval measures with values in conjugate Banach spaces which can be represented as Henstock-Kurzweil-Gelfand integrals. If the range space has the weak Radon-Nikodým property (WRNP), then we precisely describe when these integrals are in fact Henstock-Kurzweil-Pettis integrals.
A Birkhoff type integral and the Bourgain property in a locally convex space
2007
An integral, called the $Bk$-integral, for functions taking values in a locally convex space is defined. Properties of $Bk$-integrable functions are considered and the relations with other integrals are studied. Moreover the $Bk$-integrability of bounded functions is compared with the Bourgain property.
Relations among Gauge and Pettis integrals for cwk(X)-valued multifunctions
2019
The aim of this paper is to study relationships among "gauge integrals" (Henstock, Mc Shane, Birkhoff) and Pettis integral of multifunctions whose values are weakly compact and convex subsets of a general Banach space, not necessarily separable. For this purpose we prove the existence of variationally Henstock integrable selections for variationally Henstock integrable multifunctions. Using this and other known results concerning the existence of selections integrable in the same sense as the corresponding multifunctions, we obtain three decomposition theorems. As applications of such decompositions, we deduce characterizations of Henstock and ${\mathcal H}$ integrable multifunctions, toget…
Gauge integrals and selections of weakly compact valued multifunctions
2016
In the paper Henstock, McShane, Birkhoff and variationally multivalued integrals are studied for multifunctions taking values in the hyperspace of convex and weakly compact subsets of a general Banach space X. In particular the existence of selections integrable in the same sense of the corresponding multifunctions has been considered.