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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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 or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Measure theory, Beta functions, Transcendental functions
Official Date:	October 1985
Dates:	Date Event October 1985 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Schmidt, Klaus, 1943-
Format of File:	pdf
Extent:	iii, 82 leaves
Language:	eng

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