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A remark on the central limit theorem in Banach spaces

Part of the Lecture Notes in Mathematics book series (LNM,volume 1080)

Keywords

  • Banach Space
  • Central Limit Theorem
  • Random Variable Independent
  • Gaussian Random Variable
  • Preceding Theorem

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References

  1. Chobanyan, S.A., Tarieladze, V.I.: A counterexample concerning CLT in Banach spaces. Probability theory on vector spaces, Poland 1977. Lecture Notes in Math. 656, 25–30, Springer, Berlin-Heidelberg-New York (1978).

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  2. Giné, E., Zinn, J.: Central limit theorems and weak laws of large numbers in certain Banach spaces. Zeitschrift für Wahr. 62, 323–354, (1983).

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  3. Hoffmann-Jørgensen, J.: Sums of independent Banach space valued random variables. Studia Math. 52, 159–186 (1974).

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  4. Hoffmann-Jørgensen, J., Pisier, G.: The law of large numbers and the central limit theorem in Banach spaces. Ann. Probability 4, 587–599 (1976).

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  5. Ledoux, M.: Théorème limite central dans les espaces ℓp(B) (1 ≤ p<∞). Ann. Inst. H. Poincaré 19, 393–411 (1983).

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  6. Pisier, G.: Le théorème de la limite centrale et la loi du logarithme itéré dans les espaces de Banach. Séminaire Maurey-Schwartz 1975–76, exposés 3, 4 et annexe, Ecole Polytechnique, Paris (1976).

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  7. Zinn, J.: Inequalities in Banach spaces with applications to probabilistic limit theorems: a survey. Probability in Banach spaces III, Medford 1980. Lecture Notes in Math. 860, 324–329, Springer, Berlin-Heidelberg-New York (1981).

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© 1984 Springer-Verlag

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Ledoux, M. (1984). A remark on the central limit theorem in Banach spaces. In: Szynal, D., Weron, A. (eds) Probability Theory on Vector Spaces III. Lecture Notes in Mathematics, vol 1080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099791

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  • DOI: https://doi.org/10.1007/BFb0099791

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13388-9

  • Online ISBN: 978-3-540-38939-2

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