Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4614662 | Journal of Mathematical Analysis and Applications | 2016 | 16 Pages |
Abstract
In this paper we focus on the relation between Riemann integrability and weak continuity. A Banach space X is said to have the weak Lebesgue property if every Riemann integrable function from [0,1][0,1] into X is weakly continuous almost everywhere. We prove that the weak Lebesgue property is stable under ℓ1ℓ1-sums and obtain new examples of Banach spaces with and without this property. Furthermore, we characterize Dunford–Pettis operators in terms of Riemann integrability and provide a quantitative result about the size of the set of τ-continuous nonRiemann integrable functions, with τ a locally convex topology weaker than the norm topology.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Gonzalo Martínez-Cervantes,