On Repeated Sequential Closures of Constructible Functions in Valuations

摘要

The space of constructible functions form a dense subspace of the space of generalized valuations. In this note we prove a somewhat stronger property that the sequential closure, taken sufficiently many (in fact, infinitely many) times, of the former space is equal to the latter one. This stronger property is necessary for some applications in Alesker (Geom Funct Anal 20(5):1073-1143, 2010).