Kolmogorov-Tamarkin紧性定理的推广

EXTENSION OF KOLMOGOROV-TAMARKIN COMPACTNESS THEOREM

本文研究了Kolmogorov-Tamarkin的紧性问题.利用鞅收敛定理,获得了任意测度空间上的Lp空间中紧集的判别准则,推广了Lp(Rd,dx)集合为紧集的Kolmogorv-Tamarkin准则.

We study Kolmogorv-Tamarkin compactness theorem.By using martingale convergence theorem,we obtain criterion for compact set over an arbitrary measurable space Lp,which extend Kolmogorv-Tamarkin criterion when a set in Lp（Rd,dx） is compact.