Abstract
In this paper, we explore the question of weak-Riemann integrability of functions taking values in a dual Banach space and show that to ensure weak-Riemann integrability of weak*-continuous functions, it is both necessary and sufficient that the space in question be a Grothendieck space.
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Lone, N.A. On the Weak-Riemann Integrability of Weak*-Continuous Functions. Mediterr. J. Math. 14, 7 (2017). https://doi.org/10.1007/s00009-016-0803-8
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DOI: https://doi.org/10.1007/s00009-016-0803-8