This is a preview of subscription content, log in via an institution to check access.
Literature Cited
C. Castaing and M. Valadier, “Convex analysis and measurable multifunctions,” Lect. Notes Math., No. 580, Springer-Verlag, Berlin (1977).
A. D. Ioffe and V. M. Tikhomirov, Theory of Extremal Problems, North-Holland, Amsterdam (1979).
A. D. Ioffe and V. L. Levin, “Subdifferentials of convex functions,” Tr. Mosk. Mat. Obshch.,26, 3–73 (1972).
V. L. Levin, “Convex integral functionals and lifting theory,” Usp. Mat. Nauk,30, No. 2 (182), 115–178 (1975).
A. Ionescu-Tulcea and C. Ionescu-Tulcea, Topics in the Theory of Lifting, Springer-Verlag, New York (1969).
M. Neumann, “On the Strassen disintegration theorem,” Arch. Math.,29, 413–420 (1977).
L. Kantorovitch, “The method of successive approximations for functional equations,” Acta Math.,71, 63–97 (1939).
L. V. Kantorovich, B. Z. Vulikh, and A. G. Pinsker, Functional Analysis in Partially Ordered Spaces [in Russian], Gostekhizdat, Moscow (1950).
L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1977).
B. Z. Vulikh, Introduction to the Theory of Partially Ordered Spaces, Wolters-Noordhoff, Groningen (1967).
G. P. Akilov and S. S. Kutateladze, Ordered Vector Spaces [in Russian], Nauka, Novosibirsk (1978).
D. A. Vladimirov, Boolean Algebras [in Russian], Nauka, Moscow (1969).
H. H. Schaefer, Topological Vector Spaces, Springer-Verlag, New York (1971).
A. G. Kusraev and S. S. Kutateladze, “Local convex analysis,” Itogi Nauki i Tekhniki, Ser. Sov. Probl. Mat.,19, 155–204 (1982).
W. A. J. Luxemburg and A. R. Schep, “A Radon-Nikodym type theorem for positive operators and a dual,” Indagat. Mat..,40, No. 3, 357–375 (1978).
D. Maharam, “The representation of abstract integrals,” Trans. Am. Math. Soc.,75, 154–184 (1953).
D. Maharam, “On kernel representation of linear operators,” Trans. Am. Math. Soc.,79, 229–255 (1955).
A. G. Kusraev, “On a certain property of the bases of K-spaces of regular operators and some of its applications,” Preprint, Inst. Mat., Siberian Branch, Academy of Sciences of the USSR, Novosibirsk (1977).
S. S. Kutateladze, “On convex analysis in modules,” Sib. Mat. Zh.,22, No. 4, 118–128 (1981).
B. Z. Vulikh and G. Ya. Lozanovskii, “On the representation of completely linear and regular functionals in semiordered spaces,” Mat. Sb.,84, No. 3, 331–352 (1971).
A. G. Kusraev, “General disintegration formulas,” Dokl. Akad. Nauk SSSR,265, No. 6, 1312–1316 (1982).
A. G. Kusraev, “Order-continuous functionals in Boolean-valued models of the theory of sets,” Sib. Mat. Zh.,25, No. 1, 69–79 (1984).
A. G. Kusraev, “Certain applications of the theory of Boolean-valued models to functional analysis,” Preprint, Inst. Mat., Siberian Branch, Academy of Sciences of the USSR, Novosibirsk (1982).
A. G. Kusraev, “Boolean-valued analysis of the duality of extended modules,” Dokl. Akad. Nauk SSSR,267, No. 5, 1049–1052 (1982).
Additional information
Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 25, No. 5, pp. 79–89, September–October, 1984.
Rights and permissions
About this article
Cite this article
Kusraev, A.G. Abstract disintegration in Kantorovich spaces. Sib Math J 25, 749–757 (1984). https://doi.org/10.1007/BF00968688
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00968688