Convergence theorems for Banach space valued integrable multifunctions.
Convergence theorems for the Birkhoff integral
We give sufficient conditions for the interchange of the operations of limit and the Birkhoff integral for a sequence of functions from a measure space to a Banach space. In one result the equi-integrability of ’s is involved and we assume almost everywhere. The other result resembles the Lebesgue dominated convergence theorem where the almost uniform convergence of to is assumed.
Convolutions and products of partially ordered vector-valued positive measures.
Convolutions with the continuous primitive integral.
Copies of in the space of Pettis integrable functions with integrals of finite variation
Let (Ω,Σ,μ) be a complete finite measure space and X a Banach space. We show that the space of all weakly μ-measurable (classes of scalarly equivalent) X-valued Pettis integrable functions with integrals of finite variation, equipped with the variation norm, contains a copy of if and only if X does.
Correction to: Integrating bounded functions for the Dobrakov integral
Correction to the paper ’Copies of in the space of Pettis integrable functions with integrals of finite variation’ (Studia Math. 210 (2012), 93-98)
Corrigenda to: "Optimal domains for the kernel operator associated with Sobolev's inequality" (Studia Math. 158 (2003), 131-152)