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The law of the iterated logarithm for extreme value of random elements in Banach lattices. (English. Ukrainian original) Zbl 0960.60009
Theory Probab. Math. Stat. 59, 129-138 (1999); translation from Teor. Jmorvirn. Mat. Stat. 59, 125-134 (1998).
The author introduces the notions $$\lim\sup\{\cdot\}$$ and $$\lim\inf\{\cdot\}$$ in some infinite-dimensional spaces, namely, in separable Banach lattices. Using these notions the law of the iterated logarithm is generalized for these spaces. The law of the iterated logarithm for extremes of a sequence of normed random elements in a separable Banach lattice is proved. Similar problems were investigated by the author [Ukr. Math. J. 50, No. 9, 1405-1415 (1998); translation from Ukr. Mat. Zh. 50, No. 9, 1227-1235 (1998; Zbl 0941.60014)].
##### MSC:
 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case) 60F15 Strong limit theorems 60G10 Stationary stochastic processes