×

zbMATH — the first resource for mathematics

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

MSC:
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.)
PDF BibTeX XML Cite
Full Text: EuDML
References:
[1] BERNAU S. J.: Uniwue representation of Archimedean lattice groups and normal Archimedean lattice rings. Proc. London Math. Soc. 3, 15, 1965, 599-631. · Zbl 0134.10802
[2] FREMLIN D. H.: A direct proof of the Matthes-Wright integral extension theorem. J. London Math. Soc. 11, 1975, 276-284. · Zbl 0313.06016
[3] LUXEMBURG W. A., ZAANEN A. C: Riesz Spaces I. North-Holland, Amsterdam 1971. · Zbl 0231.46014
[4] RIEČAN B.: On the lattice group valued measures. Čas. pěst. mat. 101, 1976, 343-349.
[5] RIEČAN B.: On measures and integrals with values in ordered groups. Math. Slovaca 33, 1983, 2, 153-163.
[6] RIEČAN B.: On the extension of operators with values in linear semiordered spaces (Russian). Čas. pěst. mat. 93, 1968, 450-471.
[7] RIEČAN B., VOLAUF P.: On a technical lemma in lattice ordered groups. Acta Math. Univ. Comen., to appear. · Zbl 0558.06019
[8] VOLAUF P.: On extension of maps with values in ordered spaces. Math. Slovaca 30, 1980, 4, 351-361. · Zbl 0448.28007
[9] WRIGHT J. D. M.: The measure extension problem for vector lattices. Ann. Inst. Fourier, Grenoble 21, 4, 1971, 65-85. · Zbl 0215.48101
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.