Hoffmann-Jørgensen, Jørgen; Su, K.-L.; Taylor, R. L. The law of large numbers and the Itô-Nisio theorem for vector valued random fields. (English) Zbl 0870.60006 J. Theor. Probab. 10, No. 1, 145-183 (1997). Summary: Strong convergence results are obtained for vector-valued random fields. Substantial development of Banach-valued random fields and summability results are needed to provide the framework for the major results since many plausible extensions fail for multi-indexed Banach-valued random variables. This development yields general convergence results for random fields in Banach spaces, including an Itô-Nisio theorem and strong laws of large numbers. Cited in 1 Document MSC: 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case) Keywords:random field; Banach space; law of large numbers PDFBibTeX XMLCite \textit{J. Hoffmann-Jørgensen} et al., J. Theor. Probab. 10, No. 1, 145--183 (1997; Zbl 0870.60006) Full Text: DOI