Matsak I. Limit theorems for random elements in Banach lattices

The thesis is based on limit theorems for $max$-scheme of independent random elements in Banach lattices. The weak convergence of extremes inde- pendent random elements(in spaces of type $l_p$), the convergence of the distributions of integral functionals from extremes of independent random functions (in spaces of type $L_p$) and limiting distributions for probability of hitting of the extremes to order intervals for sequence of independent random functions(in spaces of type $C(Q)$) are mainly studied in this work. Asymptotic behaviour almost surely of extreme independent normal random elements in Banach lattices is also studied. Finally the new variants of the law of large numbers and the law of the iterated logarithm in the conditions of the convergence in order are entered and researched.