On Pettis integral and Radon measures

Volume 156 / 1998

Grzegorz Plebanek Fundamenta Mathematicae 156 (1998), 183-195 DOI: 10.4064/fm-156-2-183-195


Assuming the continuum hypothesis, we construct a universally weakly measurable function from [0,1] into a dual of some weakly compactly generated Banach space, which is not Pettis integrable. This (partially) solves a problem posed by Riddle, Saab and Uhl [13]. We prove two results related to Pettis integration in dual Banach spaces. We also contribute to the problem whether it is consistent that every bounded function which is weakly measurable with respect to some Radon measure is Pettis integrable.


  • Grzegorz Plebanek

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