B值鞅的一致可积条件与Banach空间的几何特性
A CONDITION OF UNIFORM INTEGRABILITY FOR B-VALUED MARTINGALES AND GEOMETRICAL PROPERTIES OF BANACH SPACES
-
摘要: 在子σ-代数列（Bn）正规情形下,本文研究了B值鞅（fn,Bn）的一致可积性与条件\lim _\lambda \rightarrow \infty \lambda P\left(S^2(f)>\lambda\right)=0之间的关系,证明了当值空间同构于q凸或p光滑空间时,两者可互推。特别当值空间同构于Hilbert空间时,两者为等价。Abstract: We study, in this paper, some relationships of condition \lim _\lambda \rightarrow \infty \lambda P\left(S^2(f)>\lambda\right)=0 and uniform integrability of B-valued martingales （fn, Bn）when the σ-algebra sequence （Bn） is regular. We prove that one of them implies another if the space which takes values in is q-convexifiable or p-smoothable, in particular, they are equivalent if the space is isomorphic to Hilbert space.
下载: