Let $M$ be an $n-$ dim compact Alexandrov space with curvature $\geq k$ with non-empty boundary $\partial M$.
Recently, a notion of generalized lower Ricci curvature bound on metric measure spaces has been defined, called $RCD^*$ condition.
Question: Does $M$ satisfy $RCD^*((n-1)k,n)$ condition ?
Remark: If M has no boundary, i.e., $\partial M=\varnothing$， then it is well known that $M$ satisfies $RCD^*((n-1)k,n)$ condition. The definition of $RCD^*$ condition is given in [1,2].
 Erbar, M., Kuwada, K., Sturm, K.: On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces. Invent. Math. 201, 993–1071 (2015)
 Ambrosio, L., Mondino, A., Savaré, G.: On the Bakry–Émery condition, the gradient estimates and the local-to global property of RCD ∗ (K, N) metric measure spaces. J. Geom. Anal. 26(1), 24–56 (2016)