On conditional compactly uniform \(p\)th-order integrability of random elements in Banach spaces (Q1612936)

Weighted sums \(\sum_{j=u_n}^{v_n}A_{nj}V_{nj}\) are investigated, where \((A_{nj})\) is an array of random variables and \((V_{nj})\) is an array of random elements in a real separable Banach space \(\mathcal{X}.\) The notion of conditional compactly uniform \(p\)th-order integrability is introduced and characterized.