A condition about almost sure convergence of martingale transforms in Banach space. (Chinese. English summary) Zbl 0781.60038
Summary: This paper considers convergence of martingale transforms
\[
\sum^ \infty_{n=1} U^{-1}_ nX_ n\text{ and }U^{-1}_ nS_ n = U^{-1}_ n\sum^ n_{i=1}X_ i
\]
in Banach space. A sufficient condition is obtained which generalizes and improves a result published earlier.
MSC:
| 60G42 | Martingales with discrete parameter |
