Inner Radius Estimates and Rigidity for a Finsler Measure Space with Boundary

In this paper, we give an estimate of the upper bound of the inner radius for a complete Finsler measure space \((M,F,\textrm{d}\mu )\) $(M,F,\text{d}\mu )$ of weighted Ricci curvature bounded from below, in terms of the \(\textrm{d}\mu \) $\text{d}\mu$ -mean curvature bound of the boundary. We also prove the rigidity result that when the boundary is compact, the upper bound is achieved if and only if M is isometric to a forward Finsler geodesic ball of vanishing radical flag curvature.