Skip to main content
Log in

Existence Conditions for Extremal Probability Measures on Polish Spaces and Some of Their Properties

  • Short Communications
  • Published:
Mathematical Notes Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. P. A. Meyer, Probability and Potentials (Blaisdell, Waltham, USA, 1966).

    MATH  Google Scholar 

  2. A. N. Shiryaev, Foundations of Stochastic Finance Mathematics (Fazis, Moscow, 1998), Vol. 1–2 [in Russian].

    Google Scholar 

  3. H. Föllmer and A. Schied, Stochastic Finance: an Introduction in Discrete Time (de Gruyter, Berlin, 2004).

    Book  Google Scholar 

  4. F. Riedel, Econometrica 77 (3), 857 (2009).

    Article  MathSciNet  Google Scholar 

  5. R. Elliott, Stochastic Calculus and Applications (Springer, Heidelberg, 1983).

    Google Scholar 

  6. A. B. Piunovskii, Optimal Control of Random Sequences in Problems with Constraints (Kluwer, Dordrecht, 1997).

    Book  Google Scholar 

  7. E. B. Dynkin and A. A. Yushkevich, Controlled Markov Processes and Applications (Nauka, Moscow, 1975) [in Russian].

    MATH  Google Scholar 

  8. N. N. Vorob’ev, Game theory. Lectures for Economists–Cyberneticists (Nauka, Moscow, 1974) [in Russian].

    Google Scholar 

  9. N. Dunford and J. Schwartz, Linear Operators, Vol. 1: General Theory (Interscience, New York, 1958).

    MATH  Google Scholar 

  10. R. Phelps, Lectures on Choquet’s Theorems (Van Nostrand, New York, 1965).

    MATH  Google Scholar 

  11. K. Floret, in Lecture Notes in Math. Vol. 801: Weakly Compact Sets (Springer- Verlag, Berlin, 1980).

    Google Scholar 

  12. S. Biagini and M. Frittelly, Ann. Appl. Probab. 18 (3), 929 (2008).

    Article  MathSciNet  Google Scholar 

  13. G. A. Vasil’ev, V. M. Khametov and E. A. Shelemekh, Math. Notes 94 (6), 963 (2013).

    Article  MathSciNet  Google Scholar 

  14. V. M. Khametov and E. A. Shelemekh, Automat. Remote Control 76 (6), 1041 (2016).

    Article  Google Scholar 

  15. A. N. Kolmogorov and S. V. Fomin, Elements of Function Theory and Functional Analysis (Nauka, Moscow, 1981) [in Russian].

    MATH  Google Scholar 

  16. V. I. Bogachev, Foundations of Measure Theory (NITs “Regular and Chaotic Dynamics,” Moscow– Izhevsk, 2003), Vol. 2 [in Russian].

    Google Scholar 

  17. J. Neveu, Bases Mathématiques du calcul des probabilités (Masson et Cie, Paris, 1964).

    MATH  Google Scholar 

  18. V. I. Bogachev, O. G. Smolyanov, and V. I. Sobolev, Vector Topology Spaces and Applications (NITs “Regular and Chaotic Dynamics,” Moscow– Izhevsk, 2012) [in Russian].

    Google Scholar 

  19. V. I. Bogachev and O. G. Smolyanov, Real and Functional Analysis: University Course (NITs “Regular and Chaotic Dynamics,” Moscow–Izhevsk, 2009) [in Russian].

    Google Scholar 

  20. V. I. Bogachev, Foundations of Measure Theory (NITs “Regular and Chaotic Dynamics,” Moscow– Izhevsk, 2003), Vol. 1 [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. A. Nesterenko.

Additional information

Translated from Matematicheskie Zametki, 2021, Vol. 109, pp. 470-474 https://doi.org/10.4213/mzm12816.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nesterenko, A.A., Khametov, V.M. & Shelemekh, E.A. Existence Conditions for Extremal Probability Measures on Polish Spaces and Some of Their Properties. Math Notes 109, 489–493 (2021). https://doi.org/10.1134/S0001434621030160

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434621030160

Keywords

Navigation