A class of discrete-time risk measures on general probability space is established. According to the properties of general probability space, we propose the conception of acceptance set and capital requirement in the static framework. Then we mainly focus on the properties of dynamic risk measures. The properties of risk measures in the static framework are introduced into the dynamic framework. In particular, three axioms about dynamic risk measures have been presented in the third section. We propose strong, middle and poor consistency properties to improve the mathematical description of dynamic risk measures on general probability space. Finally, an example for TVaR solution based on binary tree of is provided.