{"id":{"repo_id":"colostate","oai_identifier":"oai:mountainscholar.org:10217/80173"},"canonical_url":"https://search.dev.ndltd.org/etd/colostate/oai:mountainscholar.org:10217/80173","repository":{"repo_id":"colostate","name":"Colorado State University","base_url":"https://api.mountainscholar.org/server/oai/request"},"display":{"title":"Two-step coding theorem in the nearly continuous category","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Salvi, Niketa, author","Shipman, Patrick, advisor","Şahin, Ayşe, advisor","Dangelmayr, Gerhard, committee member","Oprea, Iuliana, committee member","Wang, Haonan, committee member"],"institution":"Colorado State University. 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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."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["born digital","doctoral dissertations"]},{"key":"dc:title","label":"Title","values":["Two-step coding theorem in the nearly continuous category"]}]}],"canonical_facts":{"dc:creator":["Salvi, Niketa, author","Shipman, Patrick, advisor","Şahin, Ayşe, advisor","Dangelmayr, Gerhard, committee member","Oprea, Iuliana, committee member","Wang, Haonan, committee member"],"dc:date.accessioned":["2007-01-03T05:53:57Z"],"dc:date.available":["2007-01-03T05:53:57Z"],"dc:date.issued":["2013"],"dc:description.abstract":["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. 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