We show that a general class of singular Kähler metrics with Ricci curvature bounded below define Kahler currents. In particular, the result applies to singular Kähler-Einstein metrics on klt pairs. If time permits, we would also present the RCD property for the completion of the smooth part of Kahler Einstein metric under further conditions.

This is a joint work with Shih-Kai Chiu, Max Hallgren, Gabor Székelyhidi, Tat Dat To, and Freid Tong.