Differentiability and negligible sets in Banach spaces

[摘要] 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.

[发布机构] University:University of Birmingham;Department:School of Mathematics

[关键词] Q Science;QA Mathematics