Abelian cocycles for nonsingular ergodic transformations and the genericity of type III1 transformations |
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Authors: | J R Choksi J M Hawkins V S Prasad |
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Institution: | (1) Department of Mathematics, McGill University, H3A 2K6 Montreal, Quebec, Canada;(2) Department of Mathematics, SUNY at Stony Brook, 11794 Stony Brook, NY, USA;(3) Department of Mathematics, York University, M3J 1P3 North York, Ontario, Canada |
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Abstract: | The authors prove that in the space of nonsingular transformations of a Lebesgue probability space the type III1 ergodic transformations form a denseG
set with respect to the coarse topology. They also prove that for any locally compact second countable abelian groupH, and any ergodic type III transformationT, it is generic in the space ofH-valued cocycles for the integer action given byT that the skew product ofT with the cocycle is orbit equivalent toT. Similar results are given for ergodic measure-preserving transformations as well.Research supported in part by: Nat. Sci. and Eng. Res. Council #A7163 and # U0080 F.C.A.C. Quebec, NSF Grants # MCS-8102399 and # DMS-8418431. |
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