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Inequalities in Banach spaces with applications to limit theorems in probability — A survey

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Probability in Banach Spaces III

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 860))

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References

  1. Aldous, D. (1976) A characterization of Hilbert space using the central limit theorem. J. London Math. Soc. 14, 376–380.

    Article  MathSciNet  MATH  Google Scholar 

  2. Beck, A. (1962) A convexity condition in Banach spaces and the strong law of large numbers. Proc. Amer. Math. Soc. 13, 329–334.

    Article  MathSciNet  MATH  Google Scholar 

  3. (1963) On the strong law of large numbers. Ergodic theory, F.B. Wright, ed., Academic Press, New York.

    Google Scholar 

  4. Dubinski, E., Pekcynski, A., and Rosenthal, H.P. (1972) On Banach spaces X for which π2(L∞, X)=B(L∞, X). Studia Math. 44, 617–648.

    MathSciNet  Google Scholar 

  5. Cobanyan, S.A. and Torieladze, V.I. (1977). Gaussian characterizations of certain Banach spaces. J. Multivariate Analysis 7, 183–203.

    Article  MathSciNet  Google Scholar 

  6. Dudley, R.M. (1974) Metric entropy and the central limit theorem in C(S). Ann. Inst. Fourier (Grenoble) 24, 49–60.

    Article  MathSciNet  MATH  Google Scholar 

  7. (1967) The sizes of compact subsets of Hilbert spaces and continuity of Gaussian processes. J. Funct. Analysis 1, 290–330.

    Article  MathSciNet  MATH  Google Scholar 

  8. Fortet, R.M. and Mourier, E. (1955) Les fonctions aléatoires comme éléments aléatoires dans les espaces de Banach. Studia Math. 15, 62–79.

    MathSciNet  MATH  Google Scholar 

  9. Giné, E (1974) On the central limit theorem for sample continuous processes. Ann. Prob. 2, 629–641.

    Article  MathSciNet  MATH  Google Scholar 

  10. Giné, E., Mandrekar, V., and Zinn, J. (1978). On sums of independent random variables with values in Lp 2 ≤ p<∞. Lect. Notes in Math. 709, 111–124.

    Article  Google Scholar 

  11. Hoffman-Jørgensen, J (1972) Sums of independent Banach space valued random variables Aarhus Universitet, preprint series, No. 15.

    Google Scholar 

  12. (1974) Sums of independent Banach space valued random variables. Studia Math. 52, 159–186.

    MathSciNet  MATH  Google Scholar 

  13. and Pisier, G. (1976). The strong law of large numbers and the central limit theorem in Banach spaces. Ann. Prob. 4, 587–599.

    Article  MATH  Google Scholar 

  14. Ito, K. and Nisio, M. (1968). On the convergence of sums of independent Banach space valued random variables. Osaka, J. Math. 5, 35–48.

    MathSciNet  MATH  Google Scholar 

  15. Jain, N. (1977). Central limit theorem and related questions in Banach space. Proc. of Sympos. in Pure Math. 31, 55–65.

    Article  MathSciNet  Google Scholar 

  16. and Marcus, M. (1975). Central limit theorem for C(S)-valued random variables. J. Funct. Analysis 19, 216–231.

    Article  MathSciNet  MATH  Google Scholar 

  17. and (1975) Intergrability of infinite sums of independent vector-valued random variables. Trans. Amer-Math. Soc. 212, 1–36.

    Article  MathSciNet  MATH  Google Scholar 

  18. Kahane, J.P. (1968). Some random series of functions. D.C. Heath, Boston, MA

    MATH  Google Scholar 

  19. Kwapien, S. (1972). Isomorphic characterizations of inner product spaces by orthogonal series with vector valued coefficients. Studia Math. 44, 583–595.

    MathSciNet  MATH  Google Scholar 

  20. Maurey, B. (1972) espaces de cotype 2, 0<p ≤ 2. Seminaire Maurey-Schwartz, 1972–73.

    Google Scholar 

  21. and Pisier, G. (1976). Séries de variables aléatoires vectorielles indépendantes et propriétés geometriques des espaces de Banach. Studia Math. 58, 45–90.

    MathSciNet  MATH  Google Scholar 

  22. Pisier, G. (1973) Type des espaces normés. C.R. Acad. Sc. Paris 276, 1673–1676.

    MathSciNet  MATH  Google Scholar 

  23. (1973). Sur les espaces qui ne contiennent pas de 1 1n uniformement Seminaire Maurey-Schwartz (1973–74).

    Google Scholar 

  24. and Zinn, J. (1978). On the limit theorems for random variables with values in the spaces Lp (2 ≤ p<∞). Z. Wahrscheinlichkeitstheorie verw Gebiete 41, 289–304.

    Article  MathSciNet  MATH  Google Scholar 

  25. Rosenthal, H. (1970). On the subspaces of Lp (p>2) spanned by sequences of independent random variables. Israel J. Math. 8, 273–303.

    Article  MathSciNet  MATH  Google Scholar 

  26. Strassen, V. and Dudley, R.M. (1969). The central limit theorem and ɛ-entropy, Prob. and information theory. Lect. Notes in Math. 89, 224–231.

    Article  MathSciNet  MATH  Google Scholar 

  27. Zinn, J. (1977). A note on the central limit theorem in Banach space. Ann. Prob. 5, 283–286.

    Article  MathSciNet  MATH  Google Scholar 

  28. Krivine, J.L., (1976) Sous spaces de dimension finite des espaces de Banach reticulés. Ann. of Math 104, 1–29.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Michigan State University, USA

    Joel Zinn

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  1. Joel Zinn
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Anatole Beck

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© 1981 Springer-Verlag

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Zinn, J. (1981). Inequalities in Banach spaces with applications to limit theorems in probability — A survey. In: Beck, A. (eds) Probability in Banach Spaces III. Lecture Notes in Mathematics, vol 860. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090627

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  • DOI: https://doi.org/10.1007/BFb0090627

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10822-1

  • Online ISBN: 978-3-540-38710-7

  • eBook Packages: Springer Book Archive

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