Use this URL to cite or link to this record in EThOS:
Title: Majorisation ordering of measures invariant under transformations of the interval
Author: Steel, Jacob
ISNI:       0000 0004 2697 4225
Awarding Body: Queen Mary, University of London
Current Institution: Queen Mary, University of London
Date of Award: 2010
Availability of Full Text:
Access from EThOS:
Access from Institution:
Majorisation is a partial ordering that can be applied to the set of probability measures on the unit interval I = [0, 1). Its defining property is that one measure μ majorises another measure , written μ , if R I fdμ R I fd for every convex real-valued function f : I ! R. This means that studying the majorisation of MT , the set of measures invariant under a transformation T : I ! I, can give us insight into finding the maximising and minimising T-invariant measures for convex and concave f. In this thesis I look at the majorisation ordering of MT for four categories of transformations T: concave unimodal maps, the doubling map T : x 7! 2x (mod 1), the family of shifted doubling maps T : x 7! 2x + (mod 1), and the family of orientation-reversing weakly-expanding maps.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Mathematics