An Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document} Multiplicative Coboundary Theorem for Sequences of Unitriangular Random Matrices

Bradley (J Theor Probab 9(3):659–678, 1996. https://doi.org/10.1007/BF02214081) proved a “multiplicative coboundary” theorem for sequences of unitriangular random matrices with integer entries, requiring tightness of the family of distributions of the entries from the partial matrix products of the sequence. This was an analog of Schmidt’s (Cocycles on ergodic transformation groups. Macmillan lectures in mathematics, vol 1. Macmillan Company of India, Ltd., Delhi, 1977) result for sequences of real-valued random variables with tightness of the family of partial sums. Here is an Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document} moment analog of Bradley’s result which also relaxes the restriction of entries being integers.