Riemann integrability versus weak continuity

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.