Convergence theorems for Banach space valued integrable multifunctions
type: Item
instance of: scholarly article
title: Convergence theorems for Banach space valued integrable multifunctions
zbMATH Open document ID: 0619.28009
DOI: 10.1155/S0161171287000516
author: Nikolaos S. Papageorgiou
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46178
review text: In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spaces \(L^ P_ X(\Omega)(1\leq p\leq \infty).\) Then we use that result to prove Fatou type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous convergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski-Mosco convergence of sets.
Mathematics Subject Classification ID: 28B20
Mathematics Subject Classification ID: 28B05
Mathematics Subject Classification ID: 46G10
zbMATH DE Number: 4004531
zbMATH Keywords: Bochner integrable selectors
zbMATH Keywords: weakly convergent sequence
zbMATH Keywords: Fatou type lemmata
zbMATH Keywords: dominated convergence theorems
zbMATH Keywords: Aumann integral of Banach space valued measurable multifunctions
zbMATH Keywords: Kuratowski-Mosco convergence
MaRDI profile type: Publication
OpenAlex ID: W2097932521
description: scientific article; zbMATH DE number 4004531