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## Archive of Issues

Russia Yekaterinburg
Year
2013
Issue
4
Pages
156-174
 Section Mathematics Title To question about representation of Stone compactums Author(-s) Chentsov A.G.a Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa Abstract We consider the questions connected with the representation of ultrafilters of measurable spaces and finitely additive (0,1)-measures for consequent application in extension constructions of abstract attainability problems and extremal problems. Properties connected with the application of (generalized) Cartesian products and their subspaces, and the property having the sense of the identification of ultrafilters and finitely additive (0,1)-measures and realized in the form of homeomorphism of natural topologies are investigated. Keywords extension, finitely additive measure, ultrafilter UDC 519.6 MSC 28A33 DOI 10.20537/vm130415 Received 15 May 2013 Language Russian Citation Chentsov A.G. To question about representation of Stone compactums, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 4, pp. 156-174. References Warga J. Optimal'noe upravlenie differentsial'nymi i funktsional'nymi uravneniyami (Optimal control of differential and functional equations), Moscow: Nauka, 1977, 624 p. Arkhangel’skii A.V. Compactness, Itogi Nauki i Tekhniki, Sovrem. Probl. Mat. Fund. Naprav., vol. 50, General Topology-2, Moscow: VINITI, 1989, pp. 5-128. Chentsov A.G. Ultrafilters of measurable spaces as a generalized solutions to abstract problems of attainability, Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 2011, vol. 17, no. 1, pp. 268-293. Chentsov A.G. Some constructions of the asymptotic analysis connected to the Stone-Chech compactification, Sovrem. Mat. Prilozh., 2005, vol. 26, pp. 119-150. Chentsov A.G. About the example of representation of the space of ultrafilters of the algebra of sets, Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 2011, vol. 17, no. 4, pp. 293-311. Chentsov A.G. Tiered operators and conversion based on ultrafilters, Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 2012, vol. 18, no. 4, pp. 298-314. Gamkrelidze R.V. Osnovy optimal'nogo upravleniya (Foundations of optimal control), Tbilisi: Izd. Tbil. Univ., 1975, 230 p. Krasovskii N.N., Subbotin A.I. Pozitsionnye differentsial'nye igry (Positional differential games), Moscow: Nauka, 1974, 456 p. Krasovskii N.N. Upravlenie dinamicheskoi sistemoi. Zadacha o mimimume garantirovannogo rezul'tata (Control of dynamic system. The problem of the minimum guaranteed result), Moscow: Nauka, 1985, 518 p. Subbotin A.I., Chentsov A.G. Optimizatsiya garantii v zadachakh upravleniya (Optimization of guarantee in control problems), Moscow: Nauka, 1981, 288 p. Chentsov A.G. Finitely additive measures and extensions of abstract control problems, Journal of Mathematical Sciences, 2006, vol. 133, no. 2, pp. 1045-1206. Bulinskii A.V., Shiryaev A.N. Teoriya sluchainykh protsessov (Theory of stochastic processes), Moscow: Fizmatlit, 2005, 402 p. Neve J. Matematicheskie osnovy teorii veroyatnostey (Mathematical foundations of probability theory), Moscow: Mir, 1969, 309 p. Chentsov A.G. Filters and ultrafilters in the constructions of attraction sets, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2011, no. 1, pp. 113-142. Burbaki N. Obshchaya topologiya (General topology), Moscow: Nauka, 1968, 272 p. Chentsov A.G. Elementy konechno-additivnoi teorii mery, I (The elements of finitely additive measures theory, I), Yekaterinburg: USTU-UPI, 2008, 388 p. Dunford N., Schwartz J.T. Lineinye operatopy (Linear operators), Moscow: Izd. Inostr. Lit., 1962, 895 p. Chentsov A.G. Finitely additive measures and relaxations of extremal problems, New York-London-Moscow: Plenum Publishing Corporation, 1996. Engelking R. Obshchaya topologiya (General topology), Moscow: Mir, 1986, 751 p. Chentsov A.G. To the question of the construction of correct extensions in the class of finitely additive measures, Izv. Vyssh. Uchebn. Zaved. Mat., 2002, no. 2 (477), pp. 58-80. Chentsov A.G. Asymptotic attainability, Dordrecht-Boston-London: Kluwer Academic Publishers, 1997, 322 p. Chentsov A.G. Elementy konechno-additivnoi teorii mery, II (The elements of finitely additive measures theory, II), Yekaterinburg: USTU-UPI, 2010, 541 p. Kelley J.L. Obshchaya topologiya (General topology), Moscow: Nauka, 1981, 431 p. Rudin W. Functional analysis, McGraw-Hill Science. Translated under the title Funktsional'nyi analiz, St.-Petersburg-Moscow-Krasnodar, Lan', 2005, 443 p. Chentsov A.G. To the question of the representation of the product of ultrafilters of measurable spaces, Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 2013, vol. 19, no. 2, pp. 306-318. Pashaev A.B., Chentsov A.G. Generalized control problem in the class of finitely additive measures, Kibernetika, 1986, no. 2, pp. 110-112. Chentsov A.G. To the question of the structure of the attraction sets in a topological space, Izv. Inst. Mat. Inform. Udmurt. Gos. Univ., 2012, no. 1 (39), pp. 147-150. Gryzlov A.A., Bastrykov E.S., Golovastov R.A. About points of compactification $\mathbb{N}$, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2010, no. 3, pp. 10-17. Golovastov R.A. About a bicompactification of a countable discrete space, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2011, no. 1, pp. 14-19. Full text