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Differentiability and negligible sets in Banach spaces

Dymond, Michael Robert (2014)
Ph.D. thesis, University of Birmingham.

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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:Ph.D. thesis.
Supervisor(s):Maleva, Olga
School/Faculty:Colleges (2008 onwards) > College of Engineering & Physical Sciences
Department:School of Mathematics
Subjects:QA Mathematics
Institution:University of Birmingham
ID Code:5158
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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