THE DE LA VALLÉE POUSSIN
THEOREM FOR VECTOR VALUED
MEASURE SPACES

MARÍA J. RIVERA

Abstract:

The purpose of this paper is to extend the de la Vallée Poussin theorem to ${\rm cabv}(\mu,X)$, the space of measures defined in $\Sigma$ with values in the Banach space X which are countably additive, of bounded variation and $\mu$-continuous, endowed with the variation norm.