References
P. A. Meyer, Probability and Potentials (Blaisdell, Waltham, USA, 1966).
A. N. Shiryaev, Foundations of Stochastic Finance Mathematics (Fazis, Moscow, 1998), Vol. 1–2 [in Russian].
H. Föllmer and A. Schied, Stochastic Finance: an Introduction in Discrete Time (de Gruyter, Berlin, 2004).
F. Riedel, Econometrica 77 (3), 857 (2009).
R. Elliott, Stochastic Calculus and Applications (Springer, Heidelberg, 1983).
A. B. Piunovskii, Optimal Control of Random Sequences in Problems with Constraints (Kluwer, Dordrecht, 1997).
E. B. Dynkin and A. A. Yushkevich, Controlled Markov Processes and Applications (Nauka, Moscow, 1975) [in Russian].
N. N. Vorob’ev, Game theory. Lectures for Economists–Cyberneticists (Nauka, Moscow, 1974) [in Russian].
N. Dunford and J. Schwartz, Linear Operators, Vol. 1: General Theory (Interscience, New York, 1958).
R. Phelps, Lectures on Choquet’s Theorems (Van Nostrand, New York, 1965).
K. Floret, in Lecture Notes in Math. Vol. 801: Weakly Compact Sets (Springer- Verlag, Berlin, 1980).
S. Biagini and M. Frittelly, Ann. Appl. Probab. 18 (3), 929 (2008).
G. A. Vasil’ev, V. M. Khametov and E. A. Shelemekh, Math. Notes 94 (6), 963 (2013).
V. M. Khametov and E. A. Shelemekh, Automat. Remote Control 76 (6), 1041 (2016).
A. N. Kolmogorov and S. V. Fomin, Elements of Function Theory and Functional Analysis (Nauka, Moscow, 1981) [in Russian].
V. I. Bogachev, Foundations of Measure Theory (NITs “Regular and Chaotic Dynamics,” Moscow– Izhevsk, 2003), Vol. 2 [in Russian].
J. Neveu, Bases Mathématiques du calcul des probabilités (Masson et Cie, Paris, 1964).
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].
V. I. Bogachev and O. G. Smolyanov, Real and Functional Analysis: University Course (NITs “Regular and Chaotic Dynamics,” Moscow–Izhevsk, 2009) [in Russian].
V. I. Bogachev, Foundations of Measure Theory (NITs “Regular and Chaotic Dynamics,” Moscow– Izhevsk, 2003), Vol. 1 [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Matematicheskie Zametki, 2021, Vol. 109, pp. 470-474 https://doi.org/10.4213/mzm12816.
Rights and permissions
About this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001434621030160