Corollary 45.1.9.label Let $M$ be a diffuse factor, then for each $n \in \natp$, there exist mutually orthogonal equivalent projections $\bracsn{p_j}_{1}^{2^n}\subset \text{Proj}(M)$ such that $\sum_{j = 1}^{2^n}p_{j} = 1$. If $\tau: M \to \complex$ is a tracial state, then $\tau(p_{j}) = 2^{-n}$ for all $1 \le j \le 2^{n}$.