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, k = 1, 2, . . ., formed by stochastic processes (X1, X2, . . . ,Xn), n ∈ N , the distributions of which are defined by certain Archimedean copulas. Some properties of generators of such the copulas are intensively used in our proofs. The first class of theorems stated and proved in the paper concerns sequences of ordinary maxima {Mn}, the second class of the presented results and proofs applies for sequences of the second largest maxima {

ON SOME APPLICATIONS OF THE ARCHIMEDEAN COPULAS IN THE PROOFS OF THE ALMOST SURE CENTRAL LIMIT THEOREMS FOR CERTAIN ORDER STATISTICS