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Integration of asymptotically almost periodic functions and weak asymptotic almost periodicity

SummaryWe resolve the question as to when an asymptotically almost periodic function with values in a Banach space has an asymptotically almost periodic integral. Further, we characterize the weakly relatively compact sets in spaces of vector valued continuous functions and use the resulting criteria to investigate the relationship between weak almost periodicity in the sense of Eberlein and the parallel notion utilized by Amerio in his approach to extending the classical Bohl-Bohr integration theorem....

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