GAUSSIAN MIXTURES AND NORMAL APPROXIMATION FOR V. N. SUDAKOV'S TYPICAL DISTRIBUTIONS

We derive a general upper bound on the distance of the standard normal law to typical distributions in V. N. Sudakov's theorem (in terms of the weighted total variation). Bibliography: 22 titles.
Dedicated to the memory of Vladimir Nikolaevich Sudakov 1. Introduction Let X = ([X.sub.1], ..., [X.sub.n]) be a random vector in [R.sup.n] with finite second moment and let [S.sup.n-1] = [...]