On the Fubini theorem for the Pettis integral for bounded functions (Q2725203)

There are examples which show that, in general, the Fubini Theorem fails for the Pettis integral. In this paper the author considers the validity of Fubini's Theorem for bounded Pettis integrable functions and establishes both positive and negative results. He shows that if the Banach space \(X\) is weakly compactly generated and does not contain a copy of \(\ell^{1}\), then a version of Fubini's Theorem holds for bounded Pettis integrable functions with values in \(X'\). On the other hand, he shows the existence of bounded Pettis integrable functions with values in \(\ell^{2}(\mathbb{R})\) for which Fubini's Theorem fails. There are a number of other more technical results in the paper pertaining to this problem.