Algorithmic randomness on computable metric spaces and hyperspaces

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dc.contributor.advisorBrattka, Vascoen_ZA
dc.contributor.authorBirch, Thomasen_ZA
dc.date.accessioned2016-10-04T10:09:10Z
dc.date.available2016-10-04T10:09:10Z
dc.date.issued2012en_ZA
dc.description.abstractIn this text we shall be focusing on generalizing Martin-Löf randomness to computable metric spaces with arbitrary measure (for examples of this type of generalization see Gács [14], Rojas and Hoyrup [15]. The aim of this generalization is to define algorithmic randomness on the hyperspace of non-empty compact subsets of a computable metric space, the study of which was first proposed by Barmpalias et al. [16] at the University of Florida in their work on the random closed subsets of the Cantor space. Much work has been done in the study of random sets with authors such as Diamondstone and Kjos-Hanssen [17] continuing the Florida approach, whilst others such as Axon [18] and Cenzer and Broadhead [19] have been studying the use of capacities to define hyperspace measures for use in randomness tests. Lastly in section 6.4 we shall be looking at the work done by Hertling and Weihrauch [13] on universal randomness tests in effective topological measure spaces and relate their results to randomness on computable metric measure spaces and in particular to the randomness of compact sets in the hyperspace of non-empty compact subsets of computable metric spaces.en_ZA
dc.identifier.apacitationBirch, T. (2012). <i>Algorithmic randomness on computable metric spaces and hyperspaces</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/22093en_ZA
dc.identifier.chicagocitationBirch, Thomas. <i>"Algorithmic randomness on computable metric spaces and hyperspaces."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2012. http://hdl.handle.net/11427/22093en_ZA
dc.identifier.citationBirch, T. 2012. Algorithmic randomness on computable metric spaces and hyperspaces. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Birch, Thomas AB - In this text we shall be focusing on generalizing Martin-Löf randomness to computable metric spaces with arbitrary measure (for examples of this type of generalization see Gács [14], Rojas and Hoyrup [15]. The aim of this generalization is to define algorithmic randomness on the hyperspace of non-empty compact subsets of a computable metric space, the study of which was first proposed by Barmpalias et al. [16] at the University of Florida in their work on the random closed subsets of the Cantor space. Much work has been done in the study of random sets with authors such as Diamondstone and Kjos-Hanssen [17] continuing the Florida approach, whilst others such as Axon [18] and Cenzer and Broadhead [19] have been studying the use of capacities to define hyperspace measures for use in randomness tests. Lastly in section 6.4 we shall be looking at the work done by Hertling and Weihrauch [13] on universal randomness tests in effective topological measure spaces and relate their results to randomness on computable metric measure spaces and in particular to the randomness of compact sets in the hyperspace of non-empty compact subsets of computable metric spaces. DA - 2012 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2012 T1 - Algorithmic randomness on computable metric spaces and hyperspaces TI - Algorithmic randomness on computable metric spaces and hyperspaces UR - http://hdl.handle.net/11427/22093 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/22093
dc.identifier.vancouvercitationBirch T. Algorithmic randomness on computable metric spaces and hyperspaces. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2012 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/22093en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematicsen_ZA
dc.titleAlgorithmic randomness on computable metric spaces and hyperspacesen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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