  We show that every scheme/algebraic space/stack that is quasi-compact with
quasi-finite diagonal can be approximated by a noetherian scheme/algebraic
space/stack. More generally, we show that any stack which is etale-locally a
global quotient stack can be approximated. Examples of applications are
generalizations of Chevalley's, Serre's and Zariski's theorems and Chow's lemma
to the non-noetherian setting. We also show that every quasi-compact algebraic
stack with quasi-finite diagonal has a finite generically flat cover by a
scheme.
