Bochner integrals in ordered vector spaces

Published 21 Apr 2016 in math.FA | (1604.06341v1)

Abstract: We present a natural way to cover an Archimedean directed ordered vector space $E$ by Banach spaces and extend the notion of Bochner integrability to functions with values in $E$. The resulting set of integrable functions is an Archimedean directed ordered vector space and the integral is an order preserving map.

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