This is a preview of subscription content, log in via an institution to check access.
Literature cited
L. G. Afanas'eva and Yu. I. Petunin, “The σ-algebras generated by comparable normed topologies,” Trudy Institute Matematiki VGU, No. 1 (1970).
U. Grenander, Probabilities on Algebraic Structures, Wiley, New York (1963).
N. Bourbaki, Topological Vector Spaces [Russian translation], IL, Moscow (1959).
I. I. Gikhman and A. V. Skorokhod, Theory of Stochastic Processes [in Russian], Nauka, Moscow (1971).
K. Ito and M. Nisio, “On the convergence of sums of independent Banach space valued variables,” Osaka J. Math.,5, No. 1, 35–48 (1968).
K. Kuratowski, Topology [Russian translation], Vol. 1, Mir, Moscow (1966).
S. Banach, Course of Functional Analysis [in Ukrainian], Radyans'ka Shkola, Kiev (1948).
Yu. I. Petunin, “A criterion for the reflexiveness of Banach space,” Dokl. Akad. Nauk SSSR,140, No. 1 (1961).
V. V. Buldygin, “On the convergence of stochastic sequences in Banach space,” Dokl. Akad. Nauk SSSR,213, No. 5 (1973).
J. B. Walsh, “A note on uniform convergence of stochastic processes,” Proc. Amer, Math. Soc.,18, 129–132 (1967).
J. Naresh and G. Kallianpur, “A note on uniform convergence of stochastic processes,” Proc. Amer. Math. Soc.,25, No. 4 (1970).
R. Dudley, “The sizes of compact subsets of Hilbert space and continuity of Gaussian processes,” J. of Functional Analysis,1, No. 3 (1967).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 27, No. 4, pp. 435–442, July–August, 1975.
Rights and permissions
About this article
Cite this article
Buldygin, V.V., Petunin, Y.I., Plichko, A.N. et al. On the structure of a σ-algebra of borel sets and the convergence of certain stochastic series in Banach spaces. Ukr Math J 27, 351–356 (1975). https://doi.org/10.1007/BF01085579
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01085579