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The purpose of this paper is to present Fatou type results for a sequence of Pettis integrable functions and multifunctions. We prove the non vacuity of the weak upper limit of a sequence of Pettis integrable functions taking their values in a locally convex space and we deduce a Fatou's lemma for a sequence of convex weak compact valued Pettis integrable multifunctions. We prove as well a Lebesgue theorem for a sequence of Pettis integrable multifunctions with values in the space of convex compact...
Let and be vector spaces over the same field . Following the terminology of Richard Arens [Pacific J. Math. 11 (1961), 9–23], a relation of into is called linear if and for all and . After improving and supplementing some former results on linear relations, we show that a relation of a linearly independent subset of into can be extended to a linear relation of into if and only if there exists a linear subspace of such that for all . Moreover, if generates...
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