Ensembles singuliers associés aux espaces de Banach réticulés

Abstract

With every reticulated functional Banach space is associated a quasi-topology. This notion, with a suitable countability axiom, is a generalization of the classical polish topology. The singular sets are the isolated, scattered sets etc. Which are characterized with measures carried by them. The Baire theorem also allows for a generalization. An application is made to the probabilistic model and to the potential theory.