<p> George Boole's transformation f(x)=x-1/x is an important example of a Lebesgue measure-preserving transformation of the real line. Generalized Boole transformations with finitely many singularities have been widely studied, and they are known to be measure-preserving, ergodic, conservative, pointwise ergodic, exact, and quasi-finite. We extend this work by considering a certain family of generalized Boole transformations that have infinitely many singularities. We assume that the closure of the set of singularities has Lebesgue measure zero. Transformations in this family are also known to be Lebesgue measure-preserving, and we prove that they are ergodic, conservative, pointwise dual ergodic, exact, and quasi-finite. We find the wandering rates and return sequences of these transformations, and under some further assumptions, we obtain a formula for their entropy. We also investigate the c-isomorphism of these transformations.</p>
| Identifer | oai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:10150137 |
| Date | 28 October 2016 |
| Creators | Chen, Yu-Yuan |
| Publisher | Indiana University |
| Source Sets | ProQuest.com |
| Language | English |
| Detected Language | English |
| Type | thesis |
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