Rodríguez-Salinas, Baltasar On the control measures of vector measures. (English) Zbl 1076.28011 RACSAM, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 97, No. 3, 377-384 (2003). If \(X\) is a locally convex space such that \(\{0\}\) is a \(G_{\delta}\) set, then every \(X\)-valued \(\sigma\)-additive measure on a \(\sigma\)-algebra possesses a real-valued control measure. If \(\Omega\) is uncountable then there is a measure with values in \(\mathbb R ^{\Omega}\) equipped with the product topology, which does not have a real-valued control measure. If the closed linear span of every bounded sequence in \(X\) possesses a countable total set of continuous functionals, then every \(X\)-valued Borel measure on a Lusin space has a real control measure. The conditions on the measure space and on \(X\) for existence of Rybakov type control measures are studied. Some results for polymeasures are given. Reviewer: Vladimir Kadets (Kharkov) MSC: 28B05 Vector-valued set functions, measures and integrals 46G10 Vector-valued measures and integration Keywords:vector measure; locally convex space; control measure PDFBibTeX XMLCite \textit{B. Rodríguez-Salinas}, RACSAM, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 97, No. 3, 377--384 (2003; Zbl 1076.28011) Full Text: EuDML