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Weak bases of vector measures

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We solve the problem of representation of measures with values in a Banach space as the limits of weakly convergent sequences of vector measures whose basis is a given nonnegative measure.

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References

  1. A. V. Skorokhod, Integration in Hilbert Spaces [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  2. Yu. L. Daletskii and S. V. Fomin, Measures and Differential Equations in Infinite-Dimensional Spaces [in Russian], Nauka, Moscow (1983).

    Google Scholar 

  3. H-H. Kuo, Gaussian Measures in Banach Spaces [Russian translation], Mir, Moscow (1979).

    Google Scholar 

  4. V. I. Bogachev, “Negligible sets in locally convex spaces,” Mat. Zametki, 36, No. 1, 51–64 (1984).

    MathSciNet  Google Scholar 

  5. V. I. Averbukh, O. G. Smolyanov, and S. V. Fomin, “Generalized functions and differentiable equations in linear spaces. 1. Differentiable measures,” Tr. Mosk. Mat. Obshch., 27, 133–174 (1987).

    Google Scholar 

  6. V. A. Romanov, “On H-continuous measures in a Hilbert space,” Vestn. Mosk. Univ., Ser. Mat. Mekh., 32, No. 1, 81–85 (1977).

    MathSciNet  Google Scholar 

  7. V. A. Romanov, “Vector measures of different classes of smoothness and their limits,” Ukr. Mat. Zh., 47, No. 4, 512–516 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  8. V. A. Romanov, “Limits of analytic vector measures,” Ukr. Mat. Zh., 44, No. 8, 1133–1135 (1992).

    Article  MATH  MathSciNet  Google Scholar 

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1436–1440, October, 2007.

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Romanov, V.A. Weak bases of vector measures. Ukr Math J 59, 1611–1615 (2007). https://doi.org/10.1007/s11253-008-0002-2

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  • DOI: https://doi.org/10.1007/s11253-008-0002-2

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