Uniform property $\mathrm{\Gamma }$ and finite dimensional tracial boundaries

We prove that a C${}^{\ast }$-algebra $A$ has uniform property $\mathrm{\Gamma }$ if the set of extremal tracial states, ${\mathrm{\partial }}_{e}T(A)$, is a non-empty compact space of finite covering dimension and for each $\tau \in {\mathrm{\partial }}_{e}T(A)$, the von Neumann algebra ${\pi }_{\tau }(A{)}^{\mathrm{\prime }\mathrm{\prime }}$ arising from the GNS representation has property $\mathrm{\Gamma }$.