The Stacks project

Lemma 66.45.6. A finite morphism of algebraic spaces is integral. An integral morphism of algebraic spaces which is locally of finite type is finite.

Proof. In both cases the morphism is representable, and you can check the condition after a base change by an affine scheme mapping into $Y$, see Lemmas 66.45.3. Hence this lemma follows from the same lemma for the case of schemes, see Morphisms, Lemma 29.44.4. $\square$

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