@article{VMJ_2002_4_3_a4,
author = {A. G. Kusraev and S. A. Malyugin},
title = {On the representation theorems of {A.} {D.~Aleksandrov} and {A.} {A.~Markov} for dominated operators},
journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
pages = {34--49},
year = {2002},
volume = {4},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMJ_2002_4_3_a4/}
}
TY - JOUR AU - A. G. Kusraev AU - S. A. Malyugin TI - On the representation theorems of A. D. Aleksandrov and A. A. Markov for dominated operators JO - Vladikavkazskij matematičeskij žurnal PY - 2002 SP - 34 EP - 49 VL - 4 IS - 3 UR - http://geodesic.mathdoc.fr/item/VMJ_2002_4_3_a4/ LA - ru ID - VMJ_2002_4_3_a4 ER -
A. G. Kusraev; S. A. Malyugin. On the representation theorems of A. D. Aleksandrov and A. A. Markov for dominated operators. Vladikavkazskij matematičeskij žurnal, Tome 4 (2002) no. 3, pp. 34-49. http://geodesic.mathdoc.fr/item/VMJ_2002_4_3_a4/
[1] Aleksandrov A. D., “Additive set functions in abstract spaces”, Mat. sbornik (N.S.), 8:2 (1940), 307–348 | MR | Zbl
[2] Aleksandrov A. D., “Additive set functions in abstract spaces. II; III”, Mat. sbornik (N.S.), 9:3 (1941), 563–628 | MR
[3] Aleksandrov A. D., “Additive set functions in abstract spaces, IV”, Mat. sbornik (N.S.), 13:2–3 (1943), 169–243 | MR
[4] Burbaki N., Integrirovanie. Mery na lokalno kompaktnykh prostranstvakh, prodolzhenie mery, integrirovanie mer, mery na otdelimykh prostranstvakh, Nauka, M., 1977, 600 pp.
[5] Vulikh B. Z., Vvedenie v teoriyu poluuporyadochennykh prostranstv, GIFML, M., 1961, 407 pp. | MR
[6] Vulikh B. Z., Vvedenie v teoriyu konusov v normirovannykh prostranstvakh, Izd-vo Kalininsk. gos. un-ta, Kalinin, 1977, 84 pp.
[7] Danford N., Shvarts Dzh., Lineinye operatory, v. 1, Obschaya teoriya, IL, M., 1962, 895 pp.
[8] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1984, 752 pp. | MR | Zbl
[9] Kantorovich L. V., Vulikh B. Z., Pinsker A. G., Funktsionalnyi analiz v poluuporyadochennykh prostranstvakh, Gostekhizdat, M.–L., 1950, 548 pp. | Zbl
[10] Kusraev A. G., Malyugin S. A., Nekotorye voprosy teorii vektornykh mer, Izd-vo IM SO AN SSSR, Novosibirsk, 1988, 190 pp. | MR
[11] Kusraev A. G., Malyugin S. A., “Proizvedenie i proektivnyi predel vektornykh mer”, Sovremennye problemy geometrii i analiza, Nauka, Novosibirsk, 1989, 132–152 | MR
[12] Malyugin S. A., “Kvaziradonovy mery”, Sib. mat. zhurn., 32:5 (1991), 101–111 | MR | Zbl
[13] Malyugin S. A., “Problema momentov v $K_\sigma$-prostranstve”, Sib. mat. zhurn., 34:2 (1993), 110–120 | MR | Zbl
[14] Malyugin S. A., “O liftinge kvaziradonovykh mer”, Sib. mat. zhurn., 42:2 (2001), 407–413 | MR | Zbl
[15] Markov A. A., “On mean values and exterior densities”, Mat. sb. (N.S.), 4 (1938), 165–191
[16] Khalmosh P., Teoriya mery, IL, M., 1953, 291 pp. | MR
[17] Edvards R., Funktsionalnyi analiz. Teoriya i prilozheniya, Mir, M., 1969, 1071 pp.
[18] Batt J., “Die Verallgemeinerungen des Darstellungssatzes von F. Riesz und ihre Anwendungen”, Jahresber. Deutsch. Math.-Verein., 74 (1973), 147–181 | MR | Zbl
[19] Berz E., “Verallgemeineung eines Satzes von F. Riesz”, Manuscripta Math., 2 (1970), 285–299 | DOI | MR | Zbl
[20] Christian R. R., “On order-preserving integration”, Trans. Amer. Math. Soc., 86 (1967), 463–485 | DOI | MR
[21] Diestel J., Uhl J. J., Vector measures, Series Math. Surveys, 15, Amer. Math. Soc., Providence, 1977 | MR | Zbl
[22] Dinculeanu N., Vector measures, VEB Deutscher Verlag der Wissenschaften, Berlin, 1966, 432 pp. | MR | Zbl
[23] Fremlin D. H., “A direct proof of the Matthes–Wright integral extension theorem”, J. London Math. Soc., 11:3 (1975), 276–284 | DOI | MR | Zbl
[24] Fuchssteiner B., Lusky W., Convex Cones, North-Holland, Amsterdam ets., 1981 | MR | Zbl
[25] Gray J. D., “The shaping of the Riesz representation theorem: A chapter in the history of analysis”, Arch. Hist. Exact. Sci., 31 (1984), 127–187 | DOI | MR | Zbl
[26] Kakutani S., “Concrete representation of abstract $(M)$-space”, Ann. Math., 42 (1941), 994–1024 | DOI | MR | Zbl
[27] Khurana S. S., “Lattice-valued Borel measures”, Rocky Mountain J. Math., 6:2 (1976), 377–382 | DOI | MR | Zbl
[28] Khurana S. S., “Lattice-valued Borel measures, II”, Trans. Amer. Math. Soc., 235:2 (1978), 205–211 | MR | Zbl
[29] Kirk R. B., Crenshaw J. A., “A generalized topological measure theory”, Trans. Amer. Math. Soc., 207 (1975), 189–217 | MR | Zbl
[30] Kisyński J., “Remark on strongly additive set functions”, Fund. Math., 63 (1969), 327–332 | MR
[31] Kusraev A. G., Dominated Operators, Kluwer, Dordrecht a. o., 2000, 446 pp. | MR
[32] Lipecki Z., “On strongly additive set functions”, Colloq. Math., 22:2 (1971), 255–256 | MR | Zbl
[33] Lipecki Z., “Extensions of additive set functions with values in topological group”, Bull. Acad. Polon. Sci. Sér. Sci. Math., Astronom., Phys., 12:1 (1974), 19–27 | MR
[34] Lipecki Z., Plachky D., Thomsen W., “Extensions of positive operators and extreme points, I”, Colloq. Math., 42 (1979), 279–284 | MR | Zbl
[35] Lipecki Z., “Extention of tight set functions with values in a topological group”, Bull. Acad. Polon. Sci., 22:2 (1974), 105–113 | MR | Zbl
[36] Lipecki Z., “Extension of vector-lattice homomorphisms revisited”, Indag. Math. (N.S.), 47 (1985), 229–233 | MR | Zbl
[37] Lipecki Z., “Riesz type representation theorems for positive operators”, Math. Nachr., 131 (1987), 351–356 | DOI | MR | Zbl
[38] Panchapagesan T. V., Palled Sh. V., “On vector lattice-valued measures, I”, Math. Slovaca, 33:3 (1983), 269–292 | MR | Zbl
[39] Panchapagesan T. V., Palled Sh. V., “On vector lattice-valued measures, II”, J. Austral. Math. Soc. (Ser. A), 40:2 (1986), 234–252 | DOI | MR | Zbl
[40] Pettis B. J., “On the extension of measures”, Ann. Math., 54 (1951), 186–197 | DOI | MR | Zbl
[41] Riečan B., “An extension of the Daniel integration scheme”, Mat. Ĉas., 25:3 (1975), 211–219 | MR | Zbl
[42] Riečan B., “A simplified proof of the Daniel integral extension theorem in ordered spaces”, Math. Slovaca, 32:1 (1982), 75–79 | MR | Zbl
[43] Schwartz L., Radon measures on arbitrary topological spaces and cylindrical measures, Oxford Univ. Press, London, 1983, 393 pp. | MR
[44] Seda A. K., “Integral representation of linear functionals on spaces sections”, Proc. Amer. Math. Soc., 91:4 (1984), 549–555 | MR | Zbl
[45] Semadeni Zb., Banach Spaces of Continuous Functions, Polish Scientific Publishers, Warsaw, 1971, 584 pp. | MR | Zbl
[46] Wheeler R. F., “A survey of Baire measuresand strict topologies”, Expositiones Math., 1 (1984), 97–190 | MR
[47] Wright J. D. M., “Stone algebra valued measures and integrals”, Proc. London Math. Soc., 19:3 (1969), 107–122 | DOI | MR | Zbl
[48] Wright J. D. M., “The measure extension problem for vector lattices”, Ann. Inst. Fourier (Grenoble), 21 (1971), 65–68 | MR
[49] Wright J. D. M., “Vector lattice measure on locally compact spaces”, Math. Z., 120 (1971), 193–203 | DOI | MR | Zbl
[50] Wright J. D. M., “An algebraic characterization of vector lattices with the Borel regularity property”, J. London Math. Soc., 7:2 (1973), 277–285 | DOI | MR | Zbl
[51] Wright J. D. M., “Products of positive vector measures”, Quart. J. Math., 24:94 (1973), 189–206 | DOI | MR | Zbl
[52] Wright J. D. M., “Measure with values in partially ordered spaces: regularity and $\sigma$-additivity”, Measure Theory (Oberwolfach, 1975), Lecture Notes in Math., 5, Springer, Berlin a.o., 1976, 267–276 | MR
[53] Zaanen A. C., “Measurable functions and integral operators”, Nieuw arch. wisk., 3:2 (1985), 167–205 | MR | Zbl