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Differentiability of Borel Measures Along Vector Fields on Banach Manifolds with Uniform Structure

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Ukrainian Mathematical Journal Aims and scope

We analyze the differentiability of Borel measures on Banach manifolds with uniform structure and establish a criterion of weak differentiability.

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References

  1. V. I. Bogachev, “On the Skorokhod differentiability of measures,” Teor. Veroyatn. Primen., 33, No. 2, 348–354 (1988).

    MATH  Google Scholar 

  2. V. I. Bogachev, Differentiable Measures and Malliavin Calculus [in Russian], Regulyarnaya i Khaoticheskaya Dinamika, Moscow–Izhevsk (2008).

    Google Scholar 

  3. Yu. L. Daletskii, “Stochastic differential geometry,” Usp. Mat. Nauk, 38, No. 3, 87–111 (1983).

    MathSciNet  Google Scholar 

  4. Yu. L. Daletskii and Ya. I. Belopol’skaya, Stochastic Equations and Differential Geometry [in Russian], Vyshcha Shkola, Kiev (1989).

    Google Scholar 

  5. O. G. Smolyanov and H. Weizsaecker, “Differentiable families of measures,” J. Funct. Anal., 118, 454–476 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  6. Yu. V. Bogdanskii, “Banach manifolds with bounded structure and the Gauss–Ostrogradskii formula,” Ukr. Mat. Zh., 64, No. 10, 1299–1313 (2012); English translation : Ukr. Math. J., 64, No. 10, 1475–1494 (2013).

  7. Yu. E. Gliklikh, Global and Stochastic Analysis with Applications to Mathematical Physics, Springer, London (2011).

    Book  MATH  Google Scholar 

  8. N. Bourbaki, Éléments de Mathématique. Premiere Partie. Livre III. Topologie Générale [Russian translation], Nauka, Moscow (1975).

    Google Scholar 

  9. S. Lang, Introduction to Differentiable Manifolds [Russian translation], Mir, Moscow (1967).

    Google Scholar 

  10. N. Dunford and J. T. Schwartz, Linear Operators. Part 1: General Theory [Russian translation], Inostrannaya Literatura, Moscow (1962).

    Google Scholar 

  11. N. N. Vakhaniya, V. I. Tarieladze, and S. A. Chobanyan, Probability Distributions in Banach Spaces [in Russian], Nauka, Moscow (1985).

    MATH  Google Scholar 

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

    Google Scholar 

  13. V. I. Bogachev, Foundations of Measure Theory, Vols. 1, 2 [in Russian], Regulyarnaya i Khaoticheskaya Dinamika, Moscow–Izhevsk (2006).

    Google Scholar 

  14. V. I. Bogachev, Measure Theory, Vol. 1, Springer, Berlin (2006).

    Google Scholar 

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 10, pp. 1348–1364, October, 2016.

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Moravets’ka, K.V. Differentiability of Borel Measures Along Vector Fields on Banach Manifolds with Uniform Structure. Ukr Math J 68, 1552–1573 (2017). https://doi.org/10.1007/s11253-017-1312-z

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  • DOI: https://doi.org/10.1007/s11253-017-1312-z

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