Strong laws of large numbers for arrays of orthogonal random elements in Banach spaces
This paper contains a discussion of conditions under which \({1 \over m^ \alpha n^ \beta} \sum^ m_{i = 1} \sum^ n_{j = 1} X_{ij} \to 0\) a.s., where \(\{X_{ij}\}\) is an array of orthogonal Banach space- valued random elements with suitable moment conditions. The concept of orthogonality used here is the James type. One of the major results shows that strong laws of large numbers may be obtained even in the case of real-valued random variables under weaker conditions than those usually given, the moment conditions allowing for \(p\)-th moments, \(1 \leq p \leq 2\), rather than the more usual 2nd order moments.
orthogonal Banach space-valued random elements
scientific article; zbMATH DE number 638236