A continuous flow's Bowen entropy on the generic-point set of an invariant measure is at most that measure's metric entropy, with equality when the measure is ergodic.
and Lin, S., Topological entropy for divergence points, Ergodic Theory Dynam
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On Bowen's entropy inequality and almost specification for flows
A continuous flow's Bowen entropy on the generic-point set of an invariant measure is at most that measure's metric entropy, with equality when the measure is ergodic.