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On various notions of regularity in ordered spaces. (English) Zbl 0597.28017
In the theory of linear ordered spaces X there is known a necessary and sufficient condition for the extension of every X-valued Daniell integral [J. D. M. Wright, Proc. Lond. Math. Soc., III. Ser. 19, 107-122 (1969; Zbl 0186.465)]. If X is only a lattice ordered group, the situation is another one: there are 5 different conditions used in the literature. The author examines the relationships among them.
Reviewer: B.Riečan

28B15 Set functions, measures and integrals with values in ordered spaces
28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
Zbl 0186.465
Full Text: EuDML
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