Abstract
We obtain conditions for the convergence of expressions\((\mu (A))^{ - 1} \smallint _A fd\mu \) inL 0 as the setA decreases.
References
V. N. Radchenko, “Integrals with respect to random measures, and random linear functionals,”Teor. Ver. Primen.,36, No. 3, 594–596 (1991).
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V. N. Radchenko, “Uniform integrability and Lebesgue theorem for convergence with respect toL 0-valued measures,”Ukr. Mat. Th.,48, No. 6, 857–860 (1996).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 11, pp. 1582–1585, November, 1999.
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Radchenko, V.N. Differentiability of integrals of real functions with respect toL 0-valued measures. Ukr Math J 51, 1787–1790 (1999). https://doi.org/10.1007/BF02525266
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DOI: https://doi.org/10.1007/BF02525266