unique ergodicity
A continuous map of a compact metric space is uniquely ergodic when it has exactly one invariant probability measure. Oxtoby's theorem connects this uniqueness to uniform convergence of continuous-observable time averages.
Before opening the references
Invariant Measure · Ergodic Transformation · Topological Compactness · Uniform Convergence
Where to read
Start here: MAGIC010 Ergodic Theory, Lecture 6: Continuous transformations of compact metric spaces
Charles Walkden · Lecture notes · English · Free full text
§6.8 Unique Ergodicity, definition and Theorem 6.11 (Oxtoby's ergodic theorem)
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Dynamical Systems & Ergodic Theory in the library · Preparation and skip guidance · Terminology and translation evidence