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On the Kolmogorov consistency theorem for Riesz space valued measures. (English) Zbl 0626.60007
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

MSC:
60B05 Probability measures on topological spaces
28B05 Vector-valued set functions, measures and integrals
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