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Rec. Math. [Mat. Sbornik] N.S., 1941, Volume 9(51), Number 3, Pages 563–628 (Mi msb6105)  

This article is cited in 30 scientific papers (total in 30 papers)

Additive set-functions in abstract spaces

A. D. Alexandroff


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Received: 11.10.1940
Language: English

Citation: A. D. Alexandroff, “Additive set-functions in abstract spaces”, Rec. Math. [Mat. Sbornik] N.S., 9(51):3 (1941), 563–628

Citation in format AMSBIB
\Bibitem{Ale41}
\by A.~D.~Alexandroff
\paper Additive set-functions in abstract spaces
\jour Rec. Math. [Mat. Sbornik] N.S.
\yr 1941
\vol 9(51)
\issue 3
\pages 563--628
\mathnet{http://mi.mathnet.ru/msb6105}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=5785}
\zmath{https://zbmath.org/?q=an:0028.07201|67.0163.01}


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    This publication is cited in the following articles:
    1. V. G. Evstigneev, “Bicompactness and measure”, Funct. Anal. Appl., 4:3 (1970), 213–220  mathnet  crossref  mathscinet  zmath
    2. A. A. Borovkov, “The convergence of tributions of functionals on stochastic processes”, Russian Math. Surveys, 27:1 (1972), 1–42  mathnet  crossref  mathscinet  zmath
    3. A. A. Borovkov, “Convergence of measures and random processes”, Russian Math. Surveys, 31:2 (1976), 1–69  mathnet  crossref  mathscinet  zmath
    4. F. Terpe, J. Flachsmeyer, “Some applications of the theory of compactifications of topological spaces and measure theory”, Russian Math. Surveys, 32:5 (1977), 133–171  mathnet  crossref  mathscinet  zmath
    5. V. P. Fedorova, “Linear functionals on spaces of uniformly continuous functions and abstract measures”, Russian Math. Surveys, 39:2 (1984), 153–154  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. A. K. Vidybida, “Evolution operator for the Bogolyubov (BBGKY) hierarchy. Lattice systems”, Theoret. and Math. Phys., 68:1 (1986), 681–694  mathnet  crossref  mathscinet  isi
    7. V. K. Zakharov, “Svyazi mezhdu rasshireniem Lebega i rasshireniem Borelya pervogo klassa i mezhdu sootvetstvuyuschimi im proobrazami”, Izv. AN SSSR. Ser. matem., 54:5 (1990), 928–956  mathnet  mathscinet  zmath  adsnasa; V. K. Zakharov, “Connections between the Lebesgue extension and the Borel extension of the first class, and between the preimages corresponding to them”, Math. USSR-Izv., 37:2 (1991), 273–302  crossref
    8. V. K. Zakharov, “Proobraz Gordona prostranstva Aleksandrova kak okruzhaemoe nakrytie”, Izv. RAN. Ser. matem., 56:2 (1992), 427–448  mathnet  mathscinet  zmath  adsnasa; V. K. Zakharov, “The Gordon preimage of an Aleksandrov space as an enclosed covering”, Russian Acad. Sci. Izv. Math., 40:2 (1993), 405–424  crossref  isi
    9. V. M. Klimkin, “O nekotorykh svoistvakh regulyarnykh funktsii mnozhestva”, Matem. sb., 183:6 (1992), 155–176  mathnet  mathscinet  zmath  adsnasa; V. M. Klimkin, “On some properties of regular set functions”, Russian Acad. Sci. Sb. Math., 76:1 (1993), 247–263  crossref  isi
    10. Klimkin V., Svistula M., “Uniform Boundedness of Family of Weak Regular Nonadditive Functions of a Set .2.”, Dokl. Akad. Nauk, 330:5 (1993), 554–555  isi
    11. V. K. Zakharov, “Rasshirenie Kaplana koltsa i banakhovoi algebry nepreryvnykh funktsii kak delimaya obolochka”, Izv. RAN. Ser. matem., 58:6 (1994), 51–68  mathnet  mathscinet  zmath; V. K. Zakharov, “The Kaplan extension of the ring and Banach algebra of continuous functions as a divisible hull”, Russian Acad. Sci. Izv. Math., 45:3 (1995), 477–493  crossref  isi
    12. V. K. Zakharov, “Svyaz mezhdu klassicheskim koltsom chastnykh koltsa nepreryvnykh funktsii i funktsiyami, integriruemymi po Rimanu”, Fundament. i prikl. matem., 1:1 (1995), 161–176  mathnet  mathscinet  zmath  elib
    13. V. K. Zakharov, “Extensions of the ring of continuous functions generated by regular, countably-divisible, complete rings of quotients, and their corresponding pre-images”, Izv. Math., 59:4 (1995), 677–720  mathnet  crossref  mathscinet  zmath  isi
    14. V. K. Zakharov, “Extensions of the ring of continuous functions generated by the classical, rational, and regular rings of fractions as divisible hulls”, Sb. Math., 186:12 (1995), 1773–1809  mathnet  crossref  mathscinet  zmath  isi
    15. V. M. Klimkin, T. A. Sribnaya, “Convergence of a sequence of weakly regular set functions”, Math. Notes, 62:1 (1997), 87–92  mathnet  crossref  crossref  mathscinet  zmath  isi
    16. V. K. Zakharov, A. V. Mikhalev, “The problem of general Radon representation for an arbitrary Hausdorff space”, Izv. Math., 63:5 (1999), 881–921  mathnet  crossref  crossref  mathscinet  zmath  isi
    17. Klimkin V., Klepnev D., “On the Uniform Continuity of the Family of Nonadditive Weakly Regular Set Functions”, Dokl. Math., 62:1 (2000), 14–15  isi
    18. A. I. Zhdanok, “Konechno-additivnye mery v ergodicheskoi teorii tsepei Markova. I”, Matem. tr., 4:2 (2001), 53–95  mathnet  mathscinet  zmath; A. I. Zhdanok, “Finitely Additive Measures in the Ergodic Theory of Markov Chains. I”, Siberian Adv. Math., 13:1 (2003), 87–125
    19. V. P. Fedorova, “The Stone–Weierstrass Theorem and Spaces of Measures”, Math. Notes, 72:3 (2002), 417–427  mathnet  crossref  crossref  mathscinet  zmath  isi
    20. V. K. Zakharov, A. V. Mikhalev, “The problem of general Radon representation for an arbitrary Hausdorff space. II”, Izv. Math., 66:6 (2002), 1087–1101  mathnet  crossref  crossref  mathscinet  zmath
    21. A. G. Kusraev, S. A. Malyugin, “O teoremakh predstavleniya A. D. Aleksandrova i A. A. Markova dlya mazhoriruemykh operatorov”, Vladikavk. matem. zhurn., 4:3 (2002), 34–49  mathnet  mathscinet  zmath
    22. A. I. Zhdanok, “Gamma-compactification of measurable spaces”, Siberian Math. J., 44:3 (2003), 463–476  mathnet  crossref  mathscinet  zmath  isi
    23. V. M. Klimkin, T. A. Sribnaya, “Uniform Continuity of a Family of Weakly Regular Set Functions on Topological Spaces”, Math. Notes, 74:1 (2003), 56–63  mathnet  crossref  crossref  mathscinet  zmath  isi
    24. A. E. Gutman, A. I. Sotnikov, “Order properties of the space of finitely additive transition functions”, Siberian Math. J., 45:1 (2004), 69–85  mathnet  crossref  mathscinet  zmath  isi  elib
    25. V. K. Zakharov, T. V. Rodionov, “Classification of Borel sets and functions for an arbitrary space”, Sb. Math., 199:6 (2008), 833–869  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    26. V. K. Zakharov, A. V. Mikhalev, T. V. Rodionov, “The Riesz–Radon–Fréchet problem of characterization of integrals”, Russian Math. Surveys, 65:4 (2010), 741–765  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    27. V. K. Zakharov, A. V. Mikhalëv, T. V. Rodionov, “Opisanie radonovskikh integralov kak lineinykh funktsionalov”, Fundament. i prikl. matem., 16:8 (2010), 87–161  mathnet  mathscinet; V. K. Zakharov, A. V. Mikhalev, T. V. Rodionov, “Characterization of Radon integrals as linear functionals”, J. Math. Sci., 185:2 (2012), 233–281  crossref
    28. T. A. Sribnaya, “Ravnomernaya ischerpyvaemost semeistva regulyarnykh funktsii mnozhestva v topologicheskom prostranstve”, Vestn. SamGU. Estestvennonauchn. ser., 2012, no. 9(100), 61–69  mathnet
    29. V. K. Zakharov, A. V. Mikhalëv, T. V. Rodionov, “Deskriptivnye prostranstva i prisuschie im klassy funktsii”, Fundament. i prikl. matem., 19:2 (2014), 51–107  mathnet  mathscinet; V. K. Zakharov, A. V. Mikhalev, T. V. Rodionov, “Descriptive spaces and proper classes of functions”, J. Math. Sci., 213:2 (2016), 163–200  crossref
    30. Rodionov T.V. Zakharov V.K., “A Fine Correlation Between Baire and Borel Functional Hierarchies”, Acta Math. Hung., 142:2 (2014), 384–402  crossref  isi
  • Математический сборник (новая серия) - 1936–1946
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