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Uniqueness of g-measures and the invariance of the beta-function under finitary isomorphisms, with finite expected code lengths, between g-spaces.
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Harding, Andrew (1985) Uniqueness of g-measures and the invariance of the beta-function under finitary isomorphisms, with finite expected code lengths, between g-spaces. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3067108~S15
Abstract
The following is split into two chapters. The first chapter gives a brief history concerning g-measures, their state of investigation and under what conditions, on g, unique g-measures exist. It concludes by giving equivalent conditions for a g-function to have a unique g-measure. This will, possibly, lead to a solution to Keane’s original problem about the uniqueness of a g-measure for an arbitrary g-function.
The second chapter generalises the result of Prof. K. Schmidt that the Beta-function is invariant under finitarily isomorphic (with finite expected code length) Markov spaces, to g-spaces with certain conditions on the g-function. The approach adopted is essentially that of Schmidt with slight modifications due to the more restrictive nature of the problem. The condition on the g-function, that of finite first moment variational sum, fits nicely between the two more commonly used conditions, finite variation sum and exponentially decreasing variation.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Measure theory, Beta functions, Transcendental functions | ||||
Official Date: | October 1985 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Schmidt, Klaus, 1943- | ||||
Format of File: | |||||
Extent: | iii, 82 leaves | ||||
Language: | eng |
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