Rough singular Kähler-Einstein metrics, when the metric completion is an RCD space, are equivalent to the Eyssidieux-Guedj-Zeriahi notion and imply log terminal singularities; this applies to tangent cones of noncollapsed Kähler limits.
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Remarks on Singular K\"ahler-Einstein Metrics
Rough singular Kähler-Einstein metrics, when the metric completion is an RCD space, are equivalent to the Eyssidieux-Guedj-Zeriahi notion and imply log terminal singularities; this applies to tangent cones of noncollapsed Kähler limits.