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THE COMPLETENESS IN SPACES OF BOUNDED PETTIS INTEGRABLE FUNCTIONS AND IN SPACES OF BOUNDED FUNCTIONS SATISFYING THE LAW OF LARGE NUMBERS
It has been proven already by Pettis [5] that the space P(p, X) of Pettis integrable functions may be non-complete when endowed with the semivariation norm of the integrals.Then Thomas [9] proved that the space is almost always non-complete.In view of the Open Mapping Theorem in such a case no …