Projecting the surface measure of the sphere of ℓ p n
Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 2, pp. 241-261. 
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     title = {Projecting the surface measure of the sphere of $\ell _p^n$},
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     language = {en},
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Naor, Assaf; Romik, Dan. Projecting the surface measure of the sphere of $\ell _p^n$. Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 2, pp. 241-261. doi : 10.1016/S0246-0203(02)00008-0. http://www.numdam.org/articles/10.1016/S0246-0203(02)00008-0/

[1] E. Artin, The Gamma Function, Holt, Rinehart and Winston, 1964. | MR | Zbl

[2] M. Antilla, K. Ball, I. Perissinaki, The central limit problem for convex bodies, Trans. Amer. Math. Soc., to appear. | MR | Zbl

[3] K.A. Borovkov, Convergence of projections of uniform distributions on balls, Teor. Veroyatnost. i Primenen. 35 (3) (1990) 547-551, (Russian). Translation in: , Theory Probab. Appl. 35 (3) (1991) 546-550. | MR | Zbl

[4] F. Barthe, M. Csörnyei, A. Naor, A note on simultaneous polar and Cartesian decomposition, Preprint. | MR

[5] K. Ball, I. Perissinaki, The subindependence of coordinate slabs in ℓpn balls, Israel J. Math. 107 (1998) 289-299. | MR | Zbl

[6] U. Brehm, J. Voigt, Asymptotics of cross sections of convex bodies, Beiträge Algebra Geom. 41 (2000) 437-454. | MR | Zbl

[7] P. Diaconis, D. Freedman, A dozen de Finetti-style results in search of a theory, Ann. Inst. Henri Poincaré 23 (1987) 397-423. | Numdam | MR | Zbl

[8] Y. Gordon, On Milman's inequality and random subspaces which escape through a mesh in Rn, in: Geometric Aspects of Functional Analysis (1986/87), Lecture Notes in Math., 1317, Springer, 1988, pp. 84-106. | MR | Zbl

[9] A. Koldobosky, M. Lifshits, Average volume of sections of star bodies, in: Geometric Aspects of Functional Analysis (1996-2000), Lecture Notes in Math., 1745, Springer, 2000, pp. 119-146. | Zbl

[10] P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, Cambridge University Press, 1995. | MR | Zbl

[11] A.A. Mogul'Skiĭ, de Finetti-type results for ℓp, Sibirsk. Mat. Zh. 32 (4) (1991) 88-95, (Russian). Translation in: , Siberian Math. J. 32 (4) (1992) 609-616. | MR | Zbl

[12] V. Milman, G. Schechtman, Asymptotic Theory of Finite Dimensional Normed Spaces, Springer, 1986. | MR

[13] A. Naor, The cone measure and surface measure on the sphere of ℓpn, Preprint.

[14] S.T. Rachev, Probability Metrics and the Stability of Stochastic Models, Wiley, 1991. | MR | Zbl

[15] S.T. Rachev, L. Rüschendorf, Approximate independence of distributions on spheres and their stability properties, Ann. Probab. 19 (3) (1991) 1311-1337. | MR | Zbl

[16] D. Romik, Measure concentration techniques for randomized central limit theorems, Preprint, 1998.

[17] D. Romik, Projections of product measures, Preprint, 1999.

[18] G. Schechtman, A remark concerning the dependence on ε in Dvoretzky's theorem, in: Geometric Aspects of Functional Analysis (1987/88), Lecture Notes in Math., 1376, Springer, 1989, pp. 274-277. | Zbl

[19] G. Schechtman, J. Zinn, On the volume of the intersection of two Lpn balls, Proc. Amer. Math. Soc. 110 (1) (1990) 217-224. | MR | Zbl

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