Keywords
- Central Limit Theorem
- Independent Random Variable
- Triangular Array
- Lebesgue Dominate Convergence Theorem
- Real Separable Banach Space
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
De Acosta, A., Araujo, A. and Giné, E. On Poisson measures, Gaussian measures and central limit theorem in Banach spaces. Advances in Prob. (Ed. P. Ney) (to appear).
Billingsley, P. Convergence of Probability Measures. John Wiley & Sons, 1968.
Dunford, N. and Schwartz, J.T. Linear operators I; General theory. Interscience, New York, 1958.
Hamedani, G.G. and Mandrekar, V. Central limit problem on Lp (p ≥ 2) II. Compactness of infinitely divisible laws. J. Multivariate Analysis 7 (1977) 363–373.
Hoffman-Jørgenson, J. Sums of independent Banach space valued random variables. Studia Math. 52 159–186.
Jain, N. Central limit theorem in a Banach space. Lecture Notes #526, 114–130, Springer-Verlag, New York, 1976.
Kuelbs, J. and Mandrekar, V. Harmonic analysis on F-spaces with a basis. Trans. Amer. Math. Soc. 169 113–152.
Loève, M. Probability Theory (Second Edition). D. Van Nostrand, New York, 1960.
Mandrekar, V. and Zinn, Joel. Central limit problem for symmetric case; Convergence to non-Gaussian laws. Studia Math. 67 (to appear).
Pisier, G. and Zinn, Joel. On the limit theorems for random variables with values in spaces Lp (2 ≤ p < ∞). Z. Wahrscheinlichkeitstheorie 41 (1978_) 289–304.
Rosenthal, H.P. On the span in Lp of sequences of independent random variables. Sixth Berkeley Symposium on Math. Stat. and Prob. II, University of California Press, Berkeley and Los Angeles (1972) 149–167.
Yurinskii, V.V. On infinitely divisible distributions. Theor. Probability and Appl. 19 297–308.
Zinn, J. Another approach to the weak law of large numbers. Unpublished manuscript.
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© 1979 Springer-Verlag
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Gine, E., Mandrekar, V., Zinn, J. (1979). On sums of independent random variables with values in Lp (2≤p<∞). In: Beck, A. (eds) Probability in Banach Spaces II. Lecture Notes in Mathematics, vol 709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071953
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DOI: https://doi.org/10.1007/BFb0071953
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