Convex hyperspaces of probability measures and extensors in the   asymptotic category
  The objects of the Dranishnikov asymptotic category are proper metric spaces and the morphisms are asymptotically Lipschitz maps. In this paper we provide an example of an asymptotically zero-dimensional space (in the sense of Gromov) whose space of compact convex subsets of probability measures is not an absolute extensor in the asymptotic category in the sense of Dranishnikov. 
Du\v{s}an Repov\v{s} and Mykhailo Zarichnyi
math.GN math.FA math.PR