For every continuous T on a compact space, the topological entropy equals the supremum of measure-theoretic entropies over T-invariant probabilities. Measures attaining the sup (when they exist) are measures of maximal entropy.
For every continuous T on a compact space, the topological entropy equals the supremum of measure-theoretic entropies over T-invariant probabilities. Measures attaining the sup (when they exist) are measures of maximal entropy.