Dymond, Michael Robert (2014). Differentiability and negligible sets in Banach spaces. University of Birmingham. Ph.D.
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Dymond14PhD.pdf
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Abstract
A set S in a Banach space X is called a universal differentiability set if S contains a point of differentiability of every Lipschitz function f : X -> R. The present thesis investigates the nature of such sets. We uncover examples of exceptionally small universal differentiability sets and prove that all universal differentiability sets satisfy certain strong structural conditions. Later, we expand our focus to properties of more general absolutely continuous functions.
| Type of Work: | Thesis (Doctorates > Ph.D.) | ||||||
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| Award Type: | Doctorates > Ph.D. | ||||||
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| College/Faculty: | Colleges (2008 onwards) > College of Engineering & Physical Sciences | ||||||
| School or Department: | School of Mathematics | ||||||
| Funders: | Engineering and Physical Sciences Research Council | ||||||
| Subjects: | Q Science > QA Mathematics | ||||||
| URI: | http://etheses.bham.ac.uk/id/eprint/5158 |
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