Geodesic
On Ergodic Extensions of Stationary Measures with Minimal Support
Canadian mathematical bulletin, Tome 26 (1983) no. 1, pp. 20-25

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DOI

Let T be an ergodic measure preserving transformation with the following property: there exists a positive integer n and a finite partition α such that the number of atom of is one more than that of , and the probability of at least one of the atoms is irrational. Then there exists a unique (up to conjugacy) transformation S such that there is a partition β with S restricted to isomorphic to T restricted to and the number of atoms in is one more than the number of atoms in for all m ≥ n. Moreover this transformation has discrete spectrum with at most two generators. If there are two generators, one of them must be a root of unity.
DOI : 10.4153/CMB-1983-004-8
Mots-clés : 28D05, secondary 60G10 
Krebs, William B.; Robertson, James B. On Ergodic Extensions of Stationary Measures with Minimal Support. Canadian mathematical bulletin, Tome 26 (1983) no. 1, pp. 20-25. doi: 10.4153/CMB-1983-004-8
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     author = {Krebs, William B. and Robertson, James B.},
     title = {On {Ergodic} {Extensions} of {Stationary} {Measures} with {Minimal} {Support}},
     journal = {Canadian mathematical bulletin},
     pages = {20--25},
     year = {1983},
     volume = {26},
     number = {1},
     doi = {10.4153/CMB-1983-004-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-004-8/}
}
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