B 值 L^p 极限鞅的若干性质

SOME PROPERTIES OF BANACH VALUED L^P-MARTINGALE IN THE LIMIT

本文在1≤p<∞的情形下讨论了取值于 Banach 空间的 L^p 极限鞅的收敛性质,给出了 L^p 极限鞅的 Riesz 分解,并用 L^p 极限鞅的收敛性刻划了空间的 Radon-Nikodym 性质,从而把在 p=1情形下的一些结果推广到了1≤p<∞的情形。此外,还指出了 B 值 p 拟鞅,B 值 p 一致渐近鞅与本文中的 B 值 L^p 极限鞅之间的包含关系。

This paper discusses the convergence ofL^p-martingale in the limit withvalues in Banach Space(1≤p<∞),presents to the Riesz decomposition ofL^p-martingale in the limit is given and the Radon-Nikodym property of theBanach Space is characterized with the convergence of L^p-martingale in thelimit.Thus some of resalts of L^1-marlingale in the limit are generalized.Thepaper also points out,in additiion,the relationship amon among Banach valuedp-quasi martingale,Banach valued p-uniform amart and Banaeh valued L^p-martingale in the limit.