Abstract
Let X be a Banach space and let (I, Ω, µ) be a measure space. For 1 ≤ p < ∞, let Lp (I, X) denote the space of Bochner p−integrable functions defined on I with values in X. The object of this paper is to give sufficient conditions for remotality of L1 (I, H) + L1 (I, G) in L1 (I, X), where H and G are two bounded sets in X which include as a special case remotality of L1 (I) ∧ ⊗ G + H ∧ ⊗ L1 (I) in L1 (I × I).