V. A. MARCENKO AND L. A. PASTURdistribution of this random quantity is one of the fundamental problems in the spectral analysis of random operators. Of particular interest is the case of very large Ν and n, since it often appears that for Ν -> °o the random quantity uiX; Β ρ/ (η)) converges in probability to a nonrandom number.We assume the following conditions are satisfied for Ν -> <χ>.I. The limit litnp/^mn/N = c, which for brevity we call the concentration, exists.II. The sequence of normalized spectral functions vi\; Ap/) of the operators Ap/ converges to some function v o (\) at all points of continuity: lim ν (λ;Α Ν ) = v 0 (λ).(1-2)Assuming that these conditions are satisfied, it is necessary, first of all, to make clear how the stochastic properties of operators B N {n) of the form in (1-1) ensure the convergence in probability of the sequences ν {λ; Βpj (n)) to nonrandom numbers, i.e. to explain when a nondecreasing function !/(λ; c) exists such that at all of its points of continuity

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