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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