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A characterization of almost sure convergence

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Probability in Banach Spaces II

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 709))

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References

  1. Austin, D. G., Edgar, G. A., and Ionescu Tulsea, A., "Pointwise convergence in terms of expectations," Zeit. Wahrs. verw. Gebiete, 30, pp. 17–26 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  2. Bellow, A., "Uniform amarts: A class of asymptotic martingales for which strong almost sure convergence obtains," Zeit. Wahrs. verw. Gebiete, 41, pp. 177–191 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  3. Bellow, A., "Some aspects of the theory of vector-valued amarts," Proc. Dublin Conference 1977, Vector space measures and applications I, Lecture Notes in Math. No. 644, pp. 57–67, Springer-Verlag (1978).

    Google Scholar 

  4. Bellow, A., "Sufficiently rich sets of stopping times, measurable cluster points and submartingales," Séminaire sur la géométrie des espaces de Banach, École Polytechnique 1977–1978, pp. A.1–A.11.

    Google Scholar 

  5. Brunel, A., and Sucheston, L., "Sur les amarts à valeurs vectorielles," C. R. Acad. Sci. Paris, 283, Série A, pp. 1037–1039 (1976).

    MathSciNet  MATH  Google Scholar 

  6. Chacon, R. V. and Sucheston, L., "On convergence of vector-valued asymptotic martingales," Zeit. Wahrs. verw. Gebiete, 33, pp. 55–59 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  7. Chatterji, S. D., "Martingale convergence and the Radon-Nikodym theorem in Banach spaces," Math. Scandinavica, 22, pp. 21–41 (1968).

    MathSciNet  MATH  Google Scholar 

  8. Dvoretzky, A., "On stopping time directed convergence," Bull. Amer. Math. Soc., 82, No. 2, pp. 347–349 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  9. Edgar, G. A., and Sucheston, L., "Amarts: A class of asymptotic martingales (Discrete parameter)," J. Multivariate Anal., 6, pp. 193–221 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  10. Edgar, G. A., and Sucheston, L., "Martingales in the limit and amarts," Proc. Amer. Math. Soc., 67, pp. 315–320 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  11. Meyer, P. A., Probability and potentials, Blaisdell, Waltham, Mass. 1966.

    MATH  Google Scholar 

  12. Neveu, J., Martingales à temps discret, Masson, Paris, 1972.

    Google Scholar 

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Anatole Beck

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© 1979 Springer-Verlag

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Bellow, A., Dvoretzky, A. (1979). A characterization of almost sure convergence. In: Beck, A. (eds) Probability in Banach Spaces II. Lecture Notes in Mathematics, vol 709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071947

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  • DOI: https://doi.org/10.1007/BFb0071947

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09242-1

  • Online ISBN: 978-3-540-35341-6

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