On p-adic vector measure spaces
The author has made important contributions to non-archimedean measure theory. The present paper is one of them. It is the natural continuation of his previous works about spaces of measures with values in a complete non-archimedean locally convex space \(E\). After a first preliminary section, the author studies in Section~2 the measurable sets and the integrable functions over them, with respect to a measure \(m\) defined in a separating algebra of subsets of a non-empty set and with values in \(E\). Measurable functions are introduced and treated in Section~3, where the author obtains some characterizations as well as some stability properties for this kind of functions. Finally, in Section~4, the concept of convergence in measure is given and investigated, and also several relations of this concept with the \(m\)-integrable functions are established. The study of the subject of every section is carried out in a deep and elegant way. I recommend this paper to any person interested in non-archimedean vector measure theory.
scientific article; zbMATH DE number 5673285