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Structure of measures in Lipschitz differentiability spaces
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Bate, David Stephen (2013) Structure of measures in Lipschitz differentiability spaces. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2685608~S1
Abstract
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.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Lipschitz spaces, Functional analysis | ||||
Official Date: | July 2013 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Preiss, David | ||||
Sponsors: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
Extent: | v, 91 leaves : illustrations | ||||
Language: | eng |
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