Singular Kähler-Einstein metrics on klt pairs define Kähler currents, and a tame approximation with L^p Ricci control suffices to make the metric completion an RCD space.
Strict positivity of K¨ ahler-Einstein currents, Forum of Mathematics, Sigma
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On K\"ahler-Einstein Currents
Singular Kähler-Einstein metrics on klt pairs define Kähler currents, and a tame approximation with L^p Ricci control suffices to make the metric completion an RCD space.