References
E. I. Gordon, “Nonstandard analysis and compact Abelian groups,” Sibirsk. Mat. Zh.,32, No. 2, 26–40 (1991).
E. I. Gordon, “Nonstandard analysis and locally compact Abelian groups,” Acta Appl. Math.,25, 221–239 (1991).
E. I. Gordon, “Hyperfinite approximations of commutative topological groups,” in: Advances in Analysis, Probability, and Mathematical Physics: Contributions of Nonstandard Analysis, Kluwer, Amsterdam (1993).
A. M. Vershik, “Countable groups are close to finite,” in: F. P. Greenleaf, Invariant Means on Topological Groups and Their Applications [in Russian], Mir, Moscow, 1973, pp. 112–135.
A. M. Stepin, “Approximability of groups and group actions,” Uspekhi Mat. Nauk, No. 6, 123–124 (1983).
R. I. Grigorchuk, “Degrees of growth of finitely generated groups and the theory of invariant means,” Izv. Akad. Nauk SSSR Ser. Mat.,48, No. 5, 939–985 (1984).
Ch. Champetier, L'Espace de Groups de Type Fini, Prepublications Inst. Fourier (Grenoble), No. 231, 1–19 (1993).
S. Albeverio, J. E. Fenstad et al., Nonstandard Methods in Stochastic Analysis and Mathematical Physics [Russian translation], Mir, Moscow (1990).
E. Nelson, “Internal set theory: a new approach to nonstandard analysis,” Bull. Amer. Math. Soc.,83, No. 6, 1165–1196 (1977).
A. G. Kusraev and S. S. Kutateladze, Nonstandard Methods of Analysis [in Russian], Nauka, Novosibirsk (1990).
E. Hewitt and K. Ross, Abstract Harmonic Analysis. Vol. I, II [Russian translation], Nauka, Moscow (1975).
M. A. Naĩark, Representation Theory of Groups [in Russian], Nauka, Moscow (1976).
J.-P. Serre, Linear Representations of Finite Groups [Russian translation], Mir, Moscow (1970).
Author information
Authors and Affiliations
Additional information
During the preparation of the article, the first author was supported by the International Foundation “Cultural Initiative” and the Russian Academy of Natural Sciences.
Translated from Sibirskiĩ Matematicheskiĩ, Vol. 36, No. 2, pp. 308–327, March–April, 1995.
Rights and permissions
About this article
Cite this article
Gordon, E.I., Korchagina, I.A. Hyperfinite approximations of compact groups and their representations. Sib Math J 36, 270–286 (1995). https://doi.org/10.1007/BF02110149
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02110149