Natural extensions of measurable transformations

• Main Author: Bénéteau, Catherine
• Format: Others
• Language: en
• Published: McGill University 1994
• Subjects: Mathematics.
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=22846

Given a measure-preserving transformation, one can build its natural extension, a bijective measure-preserving transformation that often shares some of the properties of the original map. Rohlin discovered that any measure-preserving transformation of a Lebesgue space has a natural extension, which can be obtained through an inverse limit process. This thesis presents Rohlin's account and develops further examples of natural extensions of non-singular transformations, one of which is an original example and one of which is an example of Silva's using the skew-product. Finally, Eigen and Silva's simple and beautiful geometric representation of a natural extension is given.