Representation of attraction elements in abstract attainability problems with asymptotic constraints

A. G. Chentsov

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2012), pp. 45-59.

Résumé

We consider an abstract attainability problem with asymptotic constraints in a topological space. We construct an extension in the class of ultrafilters of widely interpreted measurable spaces. We study an example of a static problem on the asymptotic attainability in the class of layer functions.

Détail

Keywords: attraction set, extension, topological space, ultrafilter.

Bibliographie

[1] Varga Dzh., Optimalnoe upravlenie differentsialnymi i funktsionalnymi uravneniyami, Nauka, M., 1977 | MR

[2] Golshtein E. G., Teoriya dvoistvennosti v matematicheskom programmirovanii i ee prilozheniya, Nauka, M., 1971 | MR

[3] Daffin R. Dzh., “Beskonechnye programmy”, Lineinye neravenstva i smezhnye voprosy, In. lit., M., 1959, 263–267

[4] Krasovskii N. N., Igrovye zadachi o vstreche dvizhenii, Nauka, M., 1970 | MR

[5] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974 | MR | Zbl

[6] Chentsov A. G., Finitely additive measures and relaxations of extremal problems, Plenum Publishing Corporation, New York–London–Moscow, 1996 | MR | Zbl

[7] Chentsov A. G., Asymptotic attainability, Kluwer Academic Publishers, Dordrecht–Boston–London, 1997 | MR | Zbl

[8] Chentsov A. G., “Konechno-additivnye mery i rasshireniya abstraktnykh zadach upravleniya”, Sovremennaya matematika i ee prilozh., 17, AN Gruzii, Institut kibernetiki, 2004, 3–153 | MR

[9] Chentsov A. G., “Nekotorye konstruktsii asimptoticheskogo analiza, svyazannye s kompaktifikatsiei Stouna–Chekha”, Sovremennaya matematika i ee prilozh., 26, AN Gruzii, Institut kibernetiki, 2005, 119–150 | MR

[10] Chentsov A. G., “Nesekventsialnye priblizhennye resheniya v abstraktnykh zadachakh o dostizhimosti”, Tr. In-ta matem. i mekhan. UrO RAN, 12, no. 1, Ekaterinburg, 2006, 216–241 | MR | Zbl

[11] Chentsov A. G., “Filtry i ultrafiltry v konstruktsiyakh mnozhestv prityazheniya”, Vestn. Udmurtskogo un-ta. Matematika. Mekhanika. Kompyuternye nauki, 2011, no. 1, 113–142

[12] Bulinskii A. V., Shiryaev A. N., Teoriya sluchainykh protsessov, Fizmatlit, M., 2005

[13] Burbaki N., Obschaya topologiya. Osnovnye struktury, Nauka, M., 1968 | MR

[14] Aleksandrov P. S., Vvedenie v teoriyu mnozhestv i obschuyu topologiyu, Izd-vo LKI, M., 2008 | MR

[15] Aleksandryan R. A., Mirzakhanyan E. A., Obschaya topologiya, Vyssh. shkola, M., 1979 | Zbl

[16] Kelli Dzh. L., Obschaya topologiya, Nauka, M., 1981 | MR

[17] Neve Zh., Matematicheskie osnovy teorii veroyatnostei, Mir, M., 1969 | MR | Zbl

[18] Chentsov A. G., Elementy konechno-additivnoi teorii mery, v. I, UGTU-UPI, Ekaterinburg, 2008

[19] Melentsov A. A., Baidosov V. A., Zmeev G. M., Elementy teorii mery i integrala, UrGU, Sverdlovsk, 1980

[20] Chentsov A. G., Morina S. I., Extensions and relaxations, Kluwer Academic Publishers, Dordrecht–Boston–London, 2002 | MR | Zbl

[21] Engelking R., Obschaya topologiya, Mir, M., 1986 | MR

[22] Chentsov A. G., Elementy konechno-additivnoi teorii mery, v. II, UGTU-UPI, Ekaterinburg, 2010

[23] Arkhangelskii A. V., “Kompaktnost”, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 50, VINITI, 1989, 5–128 | MR | Zbl

[24] Chentsov A. G., “Konstruirovanie operatsii predelnogo perekhoda s ispolzovaniem ultrafiltrov izmerimykh prostranstv”, Avtomatika i telemekhanika, 2007, no. 11, 208–222 | MR | Zbl

[25] Chentsov A. G., “Rasshireniya abstraktnykh zadach o dostizhimosti: nesekventsialnaya versiya”, Tr. In-ta matem. i mekhan., 13, no. 2, 2007, 184–217

[26] Chentsov A. G., “Ultrafiltry izmerimykh prostranstv kak obobschennye resheniya v abstraktnykh zadachakh o dostizhimosti”, Tr. In-ta matem. i mekhan., 17, no. 1, 2011, 268–293