Scalar curvature of definable Alexandrov spaces (Q2769463)

The author considers the definable set \(S\) [see \textit{L. van den Dries}, Tame topology and o-minimal structures. London Mathematical Society Lecture Note Series. 248. Cambridge: Cambridge Univ. Press (1998; Zbl 0953.03045)] and studies the scalar curvature measure on \(S\) -- a generalization of the integral scalar curvature measure of a Riemannian space. The main result of the paper states that if the definable set \(S\) is an Aleksandrov space of curvature \(\geq\kappa\) relative to the induced intrinsic metric of \(S\), then \(\text{scal}( S,\cdot) \geq km(m-1)\text{Vol}(\cdot) \).