We prove that for any symmetric n-dimensional normed space E and any ε. >. 0, E contains a (1. +. ε)-Euclidean subspace of dimension at least cln. n/ln(1/ε), where c is an absolute constant. The proof is based on a concentration property of order statistics of random vectors with i.i.d. coordinates.
All Science Journal Classification (ASJC) codes
- Dvoretzky's theorem
- Order statistic
- Symmetric basis