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Differentiability of integrals of real functions with respect toL 0-valued measures

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Abstract

We obtain conditions for the convergence of expressions\((\mu (A))^{ - 1} \smallint _A fd\mu \) inL 0 as the setA decreases.

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References

  1. 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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  2. P. Turpin, “Convexités dans les espaces vectorielles topologiques généraux,”Diss. Math.,131 (1976).

  3. 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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Authors and Affiliations

  1. Kiev University, Kiev

    V. N. Radchenko

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  1. V. N. Radchenko
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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

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