ON STABLE TYPE p BANACH SPACES
In the paper stable type p Banach spaces are considered. We extend a result known for independent
random variables to the mixing random variables. A sufficient and necessary condition for stable
type p Banach spaces is given.
1. Hoffmann-Jrgensen J. Sums of independent Banach space valued random variables, Studia Math. 1974,
V.52, P.159-186.
2. Kuelbs J. and Mandrekar V. Domains of attraction of stable measures on a Hilbert space. Studia Math.
1974, V.59, P.149-162.
3. Ledoux M., Talagrand M. Probability in Banach Spaces: Isoperimetry and Processes. Springer, Berlin,
1991.
4. Marcus M. B. and Woyczynski W. A. Stable measures and central limit theorems in spaces of stable type.
Transactions of the American Mathematical Society, July 1979, Volume 251, P.71-102.
5. Maurey B., Pisier G. Series de variables aleatoires vectorielles independantes et proprietes geometriques
des espaces de Banach. Stud. Math. 1976, V.58, P.45-90.
6. Pisier G. Probabilistic methods in the geometry of Banach spaces. In: Probability and Analysis, Lectures
Given at the 1st 1985 Session of the Centro Internazionale Matematico Estivo (C.I.M.E). Lecture Notes
in Mathematics, 1986, vol. 1206, P.167-241. Springer, Berlin.
7. Rosinski J. Remarks on Banach spaces of stable type. Probab. Math. Statist. 1980, 1, P.67-71.
8. Woyczynski W. A. Geometry and martingales in Banach spaces, Part II: Independent increments. In:
Kuelbs, J., Ney, P. (eds.) Probability on Banach Spaces. Advances in Probability and Related Topics,
1978, vol. 4, P.267-517. Dekker, New York.
9. Woyczynski W. A. Geometry and martingales in Banach spaces. CRC Press; 1st edition, September 30,
2020.
10. Sharipov O. Sh. On probabilistic characterization of Banach spaces by weakly dependent random elements.
Uzb. Math. 1998, J. N.2, P.86-91, (in Russian).
11. Sharipov O. Sh., Kobilov U. X. Limit theorems for weakly dependent random variables with values in
stable type p Banach spaces. Bulletin of National University of Uzbekistan: Mathematics and Natural
Sciences. 2023, Volume 6, Issue 2, P.106-119.
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