Every continuous self-map T of a compact metrisable space admits a T-invariant Borel probability measure. Proved by Cesàro-averaging any initial measure and invoking weak-* compactness. Baseline existence for all of ergodic theory.
Every continuous self-map T of a compact metrisable space admits a T-invariant Borel probability measure. Proved by Cesàro-averaging any initial measure and invoking weak-* compactness. Baseline existence for all of ergodic theory.