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Jaynes In his paper "Information theory and Statistical mechanics" says

"Previously, one constructed a theory based on equations of motion, supplemented by additional hypothesis of ergodicity, Metric transitivity, or equal a priori probabilities, and the identification of entropy was made only at the end, by comparison of the resulting equation with the laws of phenomenological thermodynamics."

In this context what does "Metric Transitivity" mean?

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It is explained on the first page of

''If E is any invariant measurable set, then either E or its complement is of measure zero.'''

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