Item 5 (0B1B)—The Stacks project

For $x \in X$ we have $\dim _ x(X) = \max \dim (Z) = \min \dim (\mathcal{O}_{X, x'})$ where the maximum is over irreducible components $Z \subset X$ containing $x$ and the minimum is over specializations $x \leadsto x'$ with $x'$ closed in $X$ .

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