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oai:mountainscholar.org:10217/801732025-12-30T03:42:39Zcom_10217_100532com_10217_100000com_10217_100468com_10217_100303col_10217_100538col_10217_100469

Salvi, Niketa, author Shipman, Patrick, advisor Şahin, Ayşe, advisor Dangelmayr, Gerhard, committee member Oprea, Iuliana, committee member Wang, Haonan, committee member 2007-01-03T05:53:57Z 2007-01-03T05:53:57Z 2013 Salvi_colostate_0053A_11885.pdf http://hdl.handle.net/10217/80173 https://doi.org/10.25675/3.019016 In measurable dynamics, one studies the measurable properties of dynamical systems. A recent surge of interest has been to study dynamical systems which have both a measurable and a topological structure. A nearly continuous Z-system consists of a Polish space X with a non-atomic Borel probability measure μ and an ergodic measure-preserving homeomorphism T on X . Let ƒ : X → R be a positive, nearly continuous function bounded away from 0 and ∞. This gives rise to a flow built over T under the function ƒ in the nearly continuous category. Rudolph proved a representation theorem in the 1970's, showing that any measurable flow, where the function ƒ is only assumed to be measure-preserving on a measurable Z-system, can be represented as a flow built under a function where the ceiling function takes only two values. We show that Rudolph's theorem holds in the nearly continuous category. born digital doctoral dissertations English eng Colorado State University. Libraries 2000-2019 Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright. flow built under a function two step flow nearly continuous Two-step coding theorem in the nearly continuous category Text Doctor of Philosophy (Ph.D.) Doctoral Mathematics Colorado State University This Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). open.access