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Projective limits of measure preserving transformations on probability spaces

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.
Year of publication:
1972
Authors: Chi, G. Y. H. ; Dinculeanu, N.
Published in:
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 2.1972, 4, p. 404-417
Publisher: Elsevier
Keywords: Projective systems inductive systems measure preserving transformations ergodicity discrete spectrum quasi-discrete spectrum rotations homomorphisms algebraic models discrete models
Type of publication: Article
Source:
Persistent link: https://www.econbiz.de/10005221495
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