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Necessary and sufficient condition for the uniform law of large numbers

Part of the Lecture Notes in Mathematics book series (LNM,volume 1153)

Keywords

  • Banach Space
  • Central Limit Theorem
  • Polish Space
  • Entropy Condition
  • Finite Cover

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References

  1. N.T. Andersen, A central limit theorem for non-separable valued functions, Mat. Inst. Aarhus University 1984, Preprint Series No.

    Google Scholar 

  2. A. Beck, On the strong law of large numbers, Ergodic Theory Proc. Int. sympt. New Orleans 1961 (ed. F.B. Wright), Academic Press

    Google Scholar 

  3. V. Dobric, Counter examples for the law of large numbers in some Banach spaces, Mat. Inst. Aarhus University, Preprint Series No.

    Google Scholar 

  4. E. Giné and J. Zinn, Some limits theorems for empirical processes, (to appear in Ann.Prob.)

    Google Scholar 

  5. J. Hoffmann-Jørgensen, Probability in B-spaces, Functional Analysis, Proc. Conf. Dobrovnik Yugoslavia 1981, Springer Verlag 1982 (LNS 948) (ed. Butkovic et al.)

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  6. J. Hoffmann-Jørgensen, Stochastic Processes on Polish spaces, (to appear)

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  7. J. Hoffman-Jørgensen, The law of large numbers for non-measurable and non-separable random elements, (to appear in Astérique)

    Google Scholar 

  8. J. Hoffmann-Jørgensen and G. Pisèer, The law of large number and the central limit theorem in Banach spaces, Ann. Prob. 4 (1976), p. 287–599

    CrossRef  Google Scholar 

  9. M. Talagrand, The Glivenko-Cantelli Problem, Preprint Ohio State University, Urbana, 1984.

    MATH  Google Scholar 

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© 1985 Springer-Verlag

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Hoffmann-Jørgensen, J. (1985). Necessary and sufficient condition for the uniform law of large numbers. In: Beck, A., Dudley, R., Hahn, M., Kuelbs, J., Marcus, M. (eds) Probability in Banach Spaces V. Lecture Notes in Mathematics, vol 1153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074954

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  • DOI: https://doi.org/10.1007/BFb0074954

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15704-5

  • Online ISBN: 978-3-540-39645-1

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