Definition 107.6.3. Let $\mathcal{X}$ be a locally Noetherian algebraic stack. Let $x \in |\mathcal{X}|$ be a finite type point. The dimension of the local ring of $\mathcal{X}$ at $x$ is $d \in \mathbf{Z}$ if the equivalent conditions of Lemma 107.6.2 are satisfied.
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