The phenomenon of measure synchronization is an important property in coupl ed Hamiltonian systems. In this paper, we investigate the measure synchronizati on in a chaotic system, and the regularity of phase difference is also discusse d in the regular coupled systems and the chaotic coupled system.A new method is proposed for determining the critical coupled strength of transition to the mea sure synchronization. At the same time, we have studied the influence of Gaussi an white noise on the measure synchronization. It is significant to investigate the conservative system using the property of measure synchronization.