Literature cited
P. De Pagter, “The components of a positive operator,” Indag. Math.,86, 229–240 (1983).
W. A. J. Luxemburg and A. C. Zaanen, Riesz Spaces, Vol. 1, Amsterdam (1971).
I. I. Shamaev, “On countable extensions of measures with values in a vector lattice,” Sib. Mat. Zh.,22, No. 3, 197–203 (1981).
L. V. Kantorovich, B. Z. Vulikh, and A. G. Pinsker, Functional Analysis in Semiordered Spaces [in Russian], Gostekhizdat, Moscow (1950).
K. Matthes, “Über die Ausdehnung positiver linearer Abbildungen,” Math. Nachr.,23, 223–257 (1961).
J. D. M. Wright, “The measure extension problem for vector lattices,” Ann. Inst. Fourier,21, No. 4, 65–85 (1971).
D. H. Fremlin, “A direct proof of the Matthas-Wright integral extension theorem,” J. London Math. Soc.,11, No. 2, 276–284 (1975).
W. A. J. Luxemburg and A. R. Schep, “An extension theorem for Riesz homomorphisms,” Indag. Math.,41, 145–154 (1979).
Z. Lipecki, D. Plachky, and W. Thomsen, “Extensions of positive operators and extreme points. I,” Colloq. Math.,42, 279–284 (1979).
Z. Lipecki and W. Thomsen, “Extensions of positive operators and extreme points. IV,” Colloq. Math..46, 269–273 (1982).
T. K. Y. C. Dodds, “Order topology and the Egoroff property in Riesz spaces,” Not. Am. Math. Soc.,16, No. 4, 644–645 (1969).
T. K. Y. C. Dodds, “Egoroff properties and the order topology in Riesz spaces,” Trans. Am. Math. Soc.,187, No. 1, 365–375 (1974).
I. P. Kostenko, “Almost uniform convergence in K-spaces,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 49–60 (1968).
D. A. Vladimirov, “On completeness of a semiordered space,” Usp. Mat. Nauk,15, No. 2, 165–172 (1960).
I. I. Shamaev, “Some order-algebraic properties of vector lattices and their connections,” Preprint, Math. Inst. Siberian Div., USSR Acad. of Sciences, Novosibirsk (1980).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 39, No. 5, pp. 757–765, May, 1986.
Rights and permissions
About this article
Cite this article
Shamaev, I.I. Countable extension of measures and σ-integrals with values in vector lattices. Mathematical Notes of the Academy of Sciences of the USSR 39, 414–418 (1986). https://doi.org/10.1007/BF01156683
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01156683