We prove that for each Bochner integrable function f there exists a trajectory yielding the Bochner integral of f, and that on infinite dimensional Banach spaces there exist Pettis integrable functions f such that no trajectory yields the Pettis integral of f.
Bongiorno, D. (2009). A first return examination of vector valued integrals.. In Operator Theory: Advances and Applications. (pp.89-97). Basel : Birkhäuser Verlag.
A first return examination of vector valued integrals.
BONGIORNO, Donatella
2009-01-01
Abstract
We prove that for each Bochner integrable function f there exists a trajectory yielding the Bochner integral of f, and that on infinite dimensional Banach spaces there exist Pettis integrable functions f such that no trajectory yields the Pettis integral of f.
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