Riečan, Juraj On the Kolmogorov consistency theorem for Riesz space valued measures. (English) Zbl 0626.60007 Acta Math. Univ. Comenianae 48-49, 173-180 (1986). The following theorem is proved. Let X be a \(\sigma\)-complete, weakly \(\sigma\)-distributive Riesz space. Let \((I,<)\) be a directed set, \(S=\{X_ a;a\in I\}^ a \)projective system and \(X_{\infty}\) its projective limit. If \(M=\{m_ a;B(X_ a)\to X\); \(a\in I\}\) is a consistent system of X- valued contents and \(m:A(X_{\infty})\to X\) an X-valued content induced by M then m is a measure. Reviewer: R.Potocky Cited in 1 ReviewCited in 3 Documents MSC: 60B05 Probability measures on topological spaces 28B05 Vector-valued set functions, measures and integrals Keywords:Kolmogorov consistency theorem; consistent system of measures; Riesz space; projective system; projective limit PDFBibTeX XMLCite \textit{J. Riečan}, Acta Math. Univ. Comenianae 48--49, 173--180 (1986; Zbl 0626.60007)