In many useful settings, having a finite Bowen-Margulis-Sullivan (BMS) measure on a flow space allows people to normalize the BMS measure into a probability measure and facilitates powerful ergodic theoretic tools. This often leads to asymptotic estimates for counting orbital points and establishing equidistribution results. Hence, it is important to know when a dynamical system admits a finite BMS measure. In this talk, I will first introduce what is a BMS measure, and then state a criterion that detects the finiteness of BMS measure on a flow space associated to a discrete subgroup of higher rank semi-simple Lie group.