Published online by Cambridge University Press: 09 April 2009
In this paper, the author generalizes the concept of thinness introduced by Kingman and Robertson (1968) to study the convexity of the range of a multimeasure. It is proved that every thin multimeasure taking values in a Fréchet space has convex range, and that, for a suitable measureable space, if a multimeasure is non-atomic, then the weak closure of its range is convex.