Abstract
For random functions that are sums of random functional series, we determine an integral over a general random measure and prove limit theorems for this integral. We consider the solution of an integral equation with respect to an unknown random measure.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. N. Radchenko, “On integrals over random measures σ-additive with probability one,”Visn. Kyiv. Univ. Mat. Mekh., Issue 31, 111–114 (1989).
P. Turpin, “Convexités dans les espaces vectorielles topologiques généraux,”Diss. Math., 131 (1976).
L. Drewnowski, “Topological rings of sets, continuous set function. III,”Bull. Acad. Pol. Sci. Sér. Sci. Math., Astron., Phys.,20, No. 6, 439–445 (1972).
N. N. Vakhaniya, V. I. Tarieladze, and S. A. Chobanyan,Probability Distributions in Banach Spaces [in Russian], Nauka, Moscow (1985).
L. Drewnowski, “Boundness of vector measures with values in the spacesL 0 of Bochner measurable functions,”Proc. Amer. Math. Soc.,91, No. 4, 581–588 (1984).
V. N. Radchenko, “Uniform integrability and the Lebesgue theorem on convergence inL 0-valued measures,”Ukr. Mat. Zh.,48, No. 6, 857–860 (1996).
Additional information
National University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 8, pp. 1087–1095, August, 1999.
Rights and permissions
About this article
Cite this article
Radchenko, V.N. Integrals of certain random functions with respect to general random measures. Ukr Math J 51, 1226–1236 (1999). https://doi.org/10.1007/BF02592510
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02592510