In this paper, a brief review of the theory of the measure extension is given in the first, then a new concept& weak semi-ring is introduced, and the measure extension on it is followed, which has generalized the Caratheodory measure extension theorem. 本文首先对测度扩张的理论做了一个简单总结,然后引进了一个新集类&弱半环,给出了其上的测度扩张定理,它推广了Caratheodory测度扩张定理。