Skip to main content
Log in

Countable extension of measures and σ-integrals with values in vector lattices

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature cited

  1. P. De Pagter, “The components of a positive operator,” Indag. Math.,86, 229–240 (1983).

    Google Scholar 

  2. W. A. J. Luxemburg and A. C. Zaanen, Riesz Spaces, Vol. 1, Amsterdam (1971).

  3. I. I. Shamaev, “On countable extensions of measures with values in a vector lattice,” Sib. Mat. Zh.,22, No. 3, 197–203 (1981).

    Google Scholar 

  4. L. V. Kantorovich, B. Z. Vulikh, and A. G. Pinsker, Functional Analysis in Semiordered Spaces [in Russian], Gostekhizdat, Moscow (1950).

    Google Scholar 

  5. K. Matthes, “Über die Ausdehnung positiver linearer Abbildungen,” Math. Nachr.,23, 223–257 (1961).

    Google Scholar 

  6. J. D. M. Wright, “The measure extension problem for vector lattices,” Ann. Inst. Fourier,21, No. 4, 65–85 (1971).

    Google Scholar 

  7. D. H. Fremlin, “A direct proof of the Matthas-Wright integral extension theorem,” J. London Math. Soc.,11, No. 2, 276–284 (1975).

    Google Scholar 

  8. W. A. J. Luxemburg and A. R. Schep, “An extension theorem for Riesz homomorphisms,” Indag. Math.,41, 145–154 (1979).

    Google Scholar 

  9. Z. Lipecki, D. Plachky, and W. Thomsen, “Extensions of positive operators and extreme points. I,” Colloq. Math.,42, 279–284 (1979).

    Google Scholar 

  10. Z. Lipecki and W. Thomsen, “Extensions of positive operators and extreme points. IV,” Colloq. Math..46, 269–273 (1982).

    Google Scholar 

  11. T. K. Y. C. Dodds, “Order topology and the Egoroff property in Riesz spaces,” Not. Am. Math. Soc.,16, No. 4, 644–645 (1969).

    Google Scholar 

  12. T. K. Y. C. Dodds, “Egoroff properties and the order topology in Riesz spaces,” Trans. Am. Math. Soc.,187, No. 1, 365–375 (1974).

    Google Scholar 

  13. I. P. Kostenko, “Almost uniform convergence in K-spaces,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 2, 49–60 (1968).

    Google Scholar 

  14. D. A. Vladimirov, “On completeness of a semiordered space,” Usp. Mat. Nauk,15, No. 2, 165–172 (1960).

    Google Scholar 

  15. I. I. Shamaev, “Some order-algebraic properties of vector lattices and their connections,” Preprint, Math. Inst. Siberian Div., USSR Acad. of Sciences, Novosibirsk (1980).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 39, No. 5, pp. 757–765, May, 1986.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01156683

Keywords

Navigation