The Stacks project

Remark 82.7.3. In Situation 82.2.1 let $X/B$ be good. Assume $X$ is integral. In this case the function field $R(X)$ of $X$ is defined and is equal to the residue field of $X$ at its generic point. See Spaces over Fields, Definition 72.4.3. Combining this with Remark 82.2.3 we find that for any $x \in X$ the residue field $\kappa (x)$ is the function field of the unique integral closed subspace $Z \subset X$ whose generic point is $x$.