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Literature Cited
F. F. Bonsall, J. Lindenstrauss, and R. R. Phelps, “Extreme positive operators on algebras of functions,” Math. Scand.,18, No. 2, 161–182 (1966).
D. K. Oates, “A noncompact Krein-Mil'man theorem,” Pac. J. Math.,36, No. 3, 781–788 (1971).
A. M. Rubinov, “Sublinear operators and operator-convex sets,” Sib. Mat. Zh.,17, No. 2, 370–380 (1976).
M. G. Krein and D. P. Mil'man, “On extreme points of retular convex sets,” Stud. Math.,9, 133–138 (1940).
D. P. Mil'man, “Facial characteristics of convex sets; extremal elements,” Tr. Mosk. Mat. Obshch.,22, 63–126 (1970).
D. A. Raikov, Vector Spaces [in Russian], Fizmatgiz, Moscow (1962).
Yu. A. Shashkin, “Convex sets, extremal points, simplexes,” in: Itogi Nauki i Tekhniki. Mat. Anal., Vol. 2, 5–50 [in Russian], VINITI, Moscow (1973).
E. M. Alfsen, Compact Convex Sets and Boundary Integrals, Springer-Verlag, Berlin (1971).
A. M. Rubinov, “Sublinear operators and their application,” Usp. Mat. Nauk.,32, No. 4, 113–174 (1977).
G. P.Akilov and S. S. Kutateladze, Ordered Vector Spaces [in Russian], Nauka, Novosibirsk (1978).
F. F. Bonsall, “Sublinear functionals and ideals in partially ordered vectors spaces,” Proc. London Math. Soc.,4, 402–418 (1954).
P. R. Andenaes, “Hahn-Banach extensions which are maximal on a given cone,” Math. Ann.,188, No. 2, 90–96 (1970).
S. Simons, “Minimal sublinear functionals,” Stud. Math.,37, No. 1, 37–56 (1970).
Additional information
Institute of Mathematics, Siberian Branch, Academy of Sciences of the USSR. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 21, No. 1, pp. 130–138, January–February, 1980.
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Kutateladze, S.S. The Krein-Mil'man theorem and its inverse. Sib Math J 21, 97–103 (1980). https://doi.org/10.1007/BF00970127
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DOI: https://doi.org/10.1007/BF00970127