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Title: Structure of measures in Lipschitz differentiability spaces
Author: Bate, David Stephen
ISNI:       0000 0004 2749 1217
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2013
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We prove the equivalence of two seemingly very di erent ways of generalising Rademacher's theorem to metric measure spaces. The rst was introduced by Cheeger and is based upon di erentiation with respect to another, xed, chart func- tion. The second approach is new for this generality and originates in some ideas of Alberti. It is based upon forming partial derivatives along a very rich structure of Lipschitz curves, analogous to the di erentiability theory of Euclidean spaces. By examining this structure further, we naturally arrive to several descriptions of Lipschitz di erentiability spaces.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council (EPSRC)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics