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We show that if X is a WGG Banach space and it does not contain any isomorphic copy of l1, then for every bounded Pettis integrable function f : [0, 1]^2 --> X* there exists a scalarly equivalent function for which the Fubini theorem for the Pettis integral holds. On the other hand, we show that for every bounded Pettis integrable function f : [0, 1]^2 --> l^2 (R) there exists a scalarly equivalent bounded function for which the Fubini theorem for the Pettis integral does not hold. We also show (assuming the Martin axiom) that there exists a bounded Pettis integrable function f : [0, 1]^2 --> L^[infinity](lambda) such that for each function g scalarly equivalent to f the function s --> g(t, s) is not weakly measurable for almost every t [belongs to] [0, 1].
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Tom
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1--14
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Bibliogr. 16 poz.,
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- Faculty of Mathematics and Computer Sciences, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland, michalak@amu.edu.pl
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bwmeta1.element.baztech-article-BAT2-0001-1229