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Uniform integrability for integrals with respect to Lo-valued measures

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Integrals of real functions with respect to Lo-valued measures are considered. It is proved that if the functions fn converge in measure to f, then ∫fn\(\int {f_n d\mu } \mathop \to \limits^P \int {fd\mu }\)fdμ if and only if some condition holds for fn, similar to the condition of uniform integrability for integrals with respect to scalar measures.

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Literature cited

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    V. M. Radchenko, “Integrals with respect to random measures that are σ-additive with probability 1,” Vīsnik Kiïv. Unīv. Ser. Mat. Mekh., No. 31, 111–114 (1989).

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 9, pp. 1264–1267, September, 1991.

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Radchenko, V.N. Uniform integrability for integrals with respect to Lo-valued measures. Ukr Math J 43, 1178–1180 (1991). https://doi.org/10.1007/BF01089220

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  • Real Function
  • Scalar Measure
  • Uniform Integrability