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.
CITATION STYLE
Bongiorno, D. (2009). A first return examination of vector-valued integrals. Operator Theory: Advances and Applications, 201, 89–97. https://doi.org/10.1007/978-3-0346-0211-2_8
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