Applications of Radon-Nikodým theorems to martingales of vector valued functions
J. J. Uhl · Bulletin of the American Mathematical Society · 1969
The purpose of this note is to announce some new martingale convergence theorems derived as consequences of the Radon-Nikod^m theorems, theorems for vector measures of Métivier [7] and Rieffel [8].The results announced here contain theorems of Scalora [9], Chatterji [l] and [2], A. and C. Ionescu-Tulcea [5] and Métivier [7].Throughout this note, unless explicitly mentioned otherwise, (Î2, S, /*) is a fixed finite measure space, 36 is a Banach space, L p (jJ>* Ï), (1 ûpU is measurable relative to JB T , and J E fr 2 dii = J E f Tl dn if T^T X and EEB TV