On the construction of correct extensions in the class of finitely additive measures

A. G. Chentsov

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2002), pp. 58-80.

Bibliographie

[1] Varga Dzh., Optimalnoe upravlenie differentsialnymi i funktsionalnymi uravneniyami, Nauka, M., 1977, 624 pp. | MR

[2] Yang L., Lektsii po variatsionnomu ischisleniyu i teorii optimalnogo upravleniya, Mir, M., 1970, 488 pp. | MR

[3] Krasovskii N. N., Teoriya upravleniya dvizheniem, Nauka, M., 1968, 475 pp. | MR

[4] Elyasberg P. E., Vvedenie v teoriyu poleta iskusstvennykh sputnikov Zemli, Nauka, M., 1965, 540 pp.

[5] Chentsov A. G., Finitely additive measures and relaxations of extremal problems, Plenum Publishing Corporation, New York–London–Moscow, 1996, 244 pp. | MR | Zbl

[6] Chentsov A. G., Asymptotic attainability, Kluwer Academic Publishers, Dordrecht–Boston–London, 1997, 322 pp. | MR | Zbl

[7] Chentsov A. G., “On approximation of asymptotic attainability domains”, Nonsmooth and discontinuos problems of control and optimization, Proc. volume from the IFAC Workshop (Chelyabinsk, Russia, 17–20 June 1998), Pergamon, 1–12

[8] Chentsov A. G., “Universal properties of generalized integral constraints in the class of finitely additive measures”, Funct. Different. Equat., 5:1–2, 69–105 | MR | Zbl

[9] Chentsov A. G., “K voprosu o korrektnom rasshirenii odnoi zadachi o vybore plotnosti veroyatnosti pri ogranicheniyakh na sistemu matematicheskikh ozhidanii”, UMN, 50:5 (1995), 223–242 | MR | Zbl

[10] Chentsov A. G., “K voprosu o korrektnom rasshirenii nekotorykh neustoichivykh zadach upravleniya s integralnymi ogranicheniyami”, Izv. RAN. Ser. matem., 63 (1999), 185–223 | MR | Zbl

[11] Danford N., Shvarts Dzh. T., Lineinye operatory. Obschaya teoriya, In. lit., M., 1962, 895 pp.

[12] Samoilenko A. M., Perestyuk N. A., Differentsialnye uravneniya s impulsnym vozdeistviem, Vischa shkola, Kiev, 1987, 287 pp.

[13] Chentsov A. G., Kashirtseva T. Yu., “Obobschennye traektorii lineinykh upravlyaemykh sistem s razryvnymi koeffitsientami pri upravlenii”, Vestn. Chelyabinsk. un-ta, 1999, no. 2, 137–146 | MR

[14] Baskakov S. I., Radiotekhnicheskie tsepi i signaly, Vyssh. shkola, M., 1988, 448 pp. | Zbl

[15] Chentsov A. G., “Konechno-additivnye mery i zadachi na minimum”, Kibernetika, 1988, no. 3, 67–70 | MR | Zbl

[16] Chentsov A. G., “Dvuznachnye mery na polualgebre mnozhestv i nekotorye ikh prilozheniya k beskonechnomernym zadacham matematicheskogo programmirovaniya”, Kibernetika, 1988, no. 6, 72–76 | MR | Zbl

[17] Chentsov A. G., “O predstavlenii mnozhestv prityazheniya, voznikayuschikh pri posledovatelnom oslablenii ogranichenii”, Dokl. RAN, 365:2 (1999), 174–177 | MR | Zbl

[18] Chentsov A. G., “Mnozhestva prityazheniya i ikh predstavlenie v vide dostizhimykh mnozhestv obobschennykh zadach”, Izv. Uralsk. gos. un-ta, 1999, no. 2, 135–153 | MR | Zbl

[19] Chentsov A. G., “Topological constructions of extensions and representations of attraction sets”, Control Dynamic Syst., Proc. Steklov Inst. Math., Suppl., 1, 35–60 | MR

[20] Kelli Dzh. L., Obschaya topologiya, Nauka, M., 1981, 431 pp. | MR

[21] Kuratovskii K., Mostovskii A., Teoriya mnozhestv, Mir, M., 1970, 416 pp. | MR

[22] Fedorchuk V. V., Filippov V. V., Obschaya topologiya. Osnovnye konstruktsii, Izd-vo Mosk. un-ta, M., 1988, 252 pp. | Zbl

[23] Engelking R., Obschaya topologiya, Mir, M., 1986, 751 pp. | MR

[24] Chentsov A. G., “Asimptoticheskaya dostizhimost pri vozmuschenii integralnykh ogranichenii v abstraktnoi zadache upravleniya, II”, Izv. vuzov. Matematika, 1995, no. 3, 62–73 | MR | Zbl

[25] Neve Zh., Matematicheskie osnovy teorii veroyatnostei, Mir, M., 1969, 309 pp. | MR | Zbl

[26] Pontryagin L. S., Obyknovennye differentsialnye uravneniya, Nauka, M., 1965, 322 pp. | MR | Zbl

[27] Bhaskara Rao K. P. S., Bhaskara Rao M., Theory of charges. A study of finitely additive measures, Acad. Press, New York, 1983, 253 pp. | MR | Zbl