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Projective limits of measure preserving transformations on probability spaces

Author

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  • Chi, G. Y. H.
  • Dinculeanu, N.

Abstract

Using the method of algebraic models, it is proved first that the projective limit T of a projective system of measure preserving transformations T[alpha] exists and is unique, modulo conjugacy, and then that if T[alpha] are ergodic with discrete spectrum, or totally ergodic (all iterates ergodic) with quasi-discrete spectrum, then T has the same property. An open problem is whether T has discrete model if all T[alpha] have discrete models.

Suggested Citation

  • Chi, G. Y. H. & Dinculeanu, N., 1972. "Projective limits of measure preserving transformations on probability spaces," Journal of Multivariate Analysis, Elsevier, vol. 2(4), pages 404-417, December.
    • Handle: RePEc:eee:jmvana:v:2:y:1972:i:4:p:404-417
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