Short Communications

Laws of large numbers in Banach spaces of type $(F,F_1 )$

A. N. Chuprunov

Kazan State University

Abstract: This paper gives strong and weak laws of large numbers for random elements with values in Banach spaces of type $(F,F_1)$. The known laws of large numbers in Banach spaces of stable and Rademacher type $p$ are special cases of these results. Characterizations of spaces of type $(F,F_1)$ are given in terms of these laws.

Keywords: space of type $(F,F_1 )$, law of large numbers, random element.

Received: 26.12.1989

 English version: Theory of Probability and its Applications, 1993, 38:4, 733–737

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