A ug 1 99 6 RANDOM VECTORS IN THE ISOTROPIC POSITION
نویسنده
چکیده
K 〈x, y〉 dy = ‖x‖ By ‖·‖ we denote the standard Euclidean norm. The notion of isotropic position was extensively studied by V. Milman and A. Pajor [M-P]. Note that our definition is consistent with [K-L-S]. The normalization in [M-P] is slightly different. If the information about the body K is uncomplete it is impossible to bring it exactly to the isotropic position. So, the definition of the isotropic position has to be modified to allow a small error. We shall say that the body K is in ε-isotropic position if for any x ∈ R (1− ε) · ‖x‖ ≤ 1 vol (K) ∫
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