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Alexandrov and Kolmogorov consistency theorem for measures with values in partially ordered groups. (English) Zbl 0820.28006
Summary: Alexandrov and Kolmogorov theorems for Riesz space value measures were discussed by E. Hrachovina [Acta. Math. Univ. Comenianae 54/55, 141-145 (1988; Zbl 0723.28004) and J. Riečan [ibid. 48/49, 173- 180 (1986; Zbl 0626.60007)]. The relations between the regularity and countable additivity for measures with values in partially ordered vector spaces were studied by J. D. M. Wright [Lect. Notes Math. 541, 267- 276 (1976; Zbl 0357.28011)]. The goal of this note is to suggest the concept of the regularity which gives the desired results for partially ordered group valued measures.

28B10 Group- or semigroup-valued set functions, measures and integrals
28B15 Set functions, measures and integrals with values in ordered spaces