Concentration of the distance in finite dimensional normed spaces

Mathematika

Volumn 45, Issue 2, 1998, Pages 245-252

  Arias De Reyna, Juan ^b   Ball, Keith M ^a   Villa, Rafael ^b  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF SEVILLE   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041777799     PISSN: 00255793     EISSN: None     Source Type: Journal    
DOI: 10.1112/s0025579300014182     Document Type: Article

References (19)

1. S. Alesker. On the Gromov-Milman theorem regarding the concentration phenomenon on uniformly convex sphere. To appear.
2. F. Barthe. Geometric and Functional Analysis. To appear.
3. J. Bastero and J. Bernués. Applications of deviation inequalities on finite metric sets. Math. Nachr., 153 (1991), 33-41.
4. ∞-cubes in finite dimensional 1-subsymmetric spaces. Rev. Mat. Univ. Complut. Madrid, 2 (1989), 47-52.
5. ∞-spaces. Seminario Dpto. Análisis Matemático, Univ. Complut. Madrid.
6. ∞-cubes in low dimensional Schatten classes. Geometric Aspects of Functional Analysis (Israel, 1992-1994), (1995), 5-11.
7. W. Beckner. Inequalities in Fourier analysis. Ann. of Math., 102 (1975), 159-182.
8. J. Bourgain, V. Milman and H. Wolfson. On type of metric spaces. Trans. Amer. Math. Soc., 294 (1986), 295-317.
9. H. J. Brascamp and E. H. Leib. Best constants in Young's inequality, its converse, and its generalization to more than three functions. Advances in Math., 20 (1976), 151-173.
10. p. Proc. Glasgow Math. Assoc., 4 (1958), 22-25.
11. T. Domínguez-Benavides. Some properties of the set and ball measures of noncompactness and applications, J. London Math. Soc. (2), 34 (1986), 120-128.
12. J. Elton and E. Odell. The unit ball of every infinite-dimensional normed linear space contains a(1 + ε)-separated sequence. Colloq. Math., 44 (1981), 105-109.
13. Z. Füredi and P. A. Loeb. On the best constant for the Besicovitch covering theorem. Proc. Amer. Math. Soc., 121 (1994), 1063-1073.
14. M. Gromov and V. D. Milman. Generalization of the spherical isoperimetric inequality to uniformly convex Banach spaces. Compositio Math., 62 (1987), 263-282.
15. C. A. Kottman. Subsets of the unit ball that are separated by more than one. Studia Math., 53 (1975), 15-27.
16. B. Maurey. Some deviation inequalities. Geom. Funct. Anal., 1 (1991), 188-197.
17. C. M. Petty. Equilateral sets in Minkowski spaces. Proc. Amer. Math. Soc., 29 (1971), 369-374.
18. M. Schmuckenschläger. A concentration of measure phenomenon on uniformly convex bodies. Geometric Aspects of Functional Analysis (Israel, 1992-1994), (1995) 275-287.
19. M. Talagrand. A new isoperimetric inequality and the concentration of measure phenomenon. Geometric Aspects of Functional Analysis (Israel Seminar, 1989-1990). Lecture Notes in Math., 1469 (1991), 94-124.