Compact dynamical systems with partial specification have average shadowing; if surjective, their ergodic measures are dense in the invariant measures.
E ven the vague specification property implies density of ergodic measures
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The interplay between partial specification, average shadowing, and Besicovitch completeness
Compact dynamical systems with partial specification have average shadowing; if surjective, their ergodic measures are dense in the invariant measures.