Projecting the surface measure of the sphere of ${\ell }_p^n$

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1. [1] E. Artin, The Gamma Function, Holt, Rinehart and Winston, 1964. Zbl0144.06802MR165148
2. [2] M. Antilla, K. Ball, I. Perissinaki, The central limit problem for convex bodies, Trans. Amer. Math. Soc., to appear. Zbl1033.52003MR2031057
3. [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. Zbl0735.60018MR1091211
4. [4] F. Barthe, M. Csörnyei, A. Naor, A note on simultaneous polar and Cartesian decomposition, Preprint. Zbl1036.52004MR2182664
5. [5] K. Ball, I. Perissinaki, The subindependence of coordinate slabs in ℓpn balls, Israel J. Math.107 (1998) 289-299. Zbl0918.60013MR1658571
6. [6] U. Brehm, J. Voigt, Asymptotics of cross sections of convex bodies, Beiträge Algebra Geom.41 (2000) 437-454. Zbl0983.52004MR1801435
7. [7] P. Diaconis, D. Freedman, A dozen de Finetti-style results in search of a theory, Ann. Inst. Henri Poincaré23 (1987) 397-423. Zbl0619.60039MR898502
8. [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. Zbl0651.46021MR950977
9. [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. Zbl0973.52002
10. [10] P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, Cambridge University Press, 1995. Zbl0819.28004MR1333890
11. [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. Zbl0778.60013MR1142071
12. [12] V. Milman, G. Schechtman, Asymptotic Theory of Finite Dimensional Normed Spaces, Springer, 1986. Zbl0606.46013MR856576
13. [13] A. Naor, The cone measure and surface measure on the sphere of ℓpn, Preprint. Zbl1109.60006
14. [14] S.T. Rachev, Probability Metrics and the Stability of Stochastic Models, Wiley, 1991. Zbl0744.60004MR1105086
15. [15] S.T. Rachev, L. Rüschendorf, Approximate independence of distributions on spheres and their stability properties, Ann. Probab.19 (3) (1991) 1311-1337. Zbl0732.62014MR1112418
16. [16] D. Romik, Measure concentration techniques for randomized central limit theorems, Preprint, 1998. 
17. [17] D. Romik, Projections of product measures, Preprint, 1999. 
18. [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. Zbl0679.46011
19. [19] G. Schechtman, J. Zinn, On the volume of the intersection of two Lpn balls, Proc. Amer. Math. Soc.110 (1) (1990) 217-224. Zbl0704.60017MR1015684