EMBEDDING C0IN THE SPACE OF PETTIS INTEGRABLE FUNCTIONS

摘要

We show that the normed space of #x3BC;-measurable Pettis integrable functions on a probability space with values in a Banach spaceXcontains a copy of the sequence spacec0if and only ifXcontains a copy ofc0.In this case, if the probability #x3BC; has infinite range, a copy ofc0consisting of #x3BC;-measurable functions can be found, such that it is complemented in the bigger space of all weakly #x3BC;-measurable Pettis integrable functions.