Dear Bruno,

You might find this online available book " An Outline of Ergodic Theory by Steven Arthur Kalikow <math.unc.edu/Faculty/petersen/erg3.doc>" math.unc.edu/Faculty/petersen/erg3.docto possible address the measure problem.

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Onward!

Stephen

"Nature, to be commanded, must be obeyed."
~ Francis Bacon

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