prove uniformly integrable local martingale is uniformly martingale

最近遇到一道题不会做，希望会的人帮忙解答下，谢谢啦！

for 0 <=t <= T < infinity,
Z_t is continous local martingale;
Z_t is Lp bounded (p >1): E[sup_{t<] < infinity;

how to get Z_t is continous uniformly integrable martingale on 0 <=t <= T ?