Summary
The question considered is the following: If two invertible measure preserving point transformations commute, in what sense is one a function of the other? The main theorem is the following: If two invertible measure preserving transformations commute, and if the first admits of approximation by periodic transformations, then the second transformation is a piecewise power of the first, where we say that σ is a piecewise power of Τ if there exists a sequence [j(n)] of positive integers such that for each measurable set A the limit of the measure of the symmetric difference of Τ (A) and σ j(n) (A) tends to zero.
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Research supported in part by NSF grant GP-3752.
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Chacon, R.V., Schwartzbauer, T. Commuting point transformations. Z. Wahrscheinlichkeitstheorie verw Gebiete 11, 277–287 (1969). https://doi.org/10.1007/BF00531651
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DOI: https://doi.org/10.1007/BF00531651