On the Radon-Nikodym property for vector measures and extensions of transfunctions (Q2035013)

Let $E$ be a Banach space and $(X,S)$ a measurable space. The authors consider vector measures of the form $\sum_n v_n m_n$, where the $v_n$ are elements of $E$ and $m_n$ are positive measures on $X$, and give a characterization of the Radon-Nikodym property. Using this result, the authors give a new proof of the Lewis-Stegall theorem. In the second part of the paper, the authors define extensions of transfunctions to vector measures and discuss the question of uniqueness of such extensions.