# Krylov-Bogolubov theorem

Any continuous map on a metrizable compact topological space has an invariant Borel probability measure (i.e. a Borel probability measure that is preserved by the given map).

Title Krylov-Bogolubov theorem KrylovBogolubovTheorem 2013-03-22 14:07:10 2013-03-22 14:07:10 Koro (127) Koro (127) 5 Koro (127) Theorem msc 37A05 msc 28C15 existence of invariant measures Krylov-Bogoliubov