We introduce the Feldman-Katok pseudometric (FK-pseudometric for short) for flows. We then provide a characterization of zero entropy loosely Bernoulli measures for continuous flows via the FK-pseudometric extending the result known for discrete-time dynamical systems. We also provide a purely topological characterization of uniquely ergodic continuous flows whose unique invariant measure is zero entropy loosely Bernoulli.
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Alexandre Trilles (2024) studied this question.
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