On the structure of universal differentiability sets

[摘要] A subset of $\\mathbb R^{d}$ is called a universal differentiability set if it contains a point of differentiability of every Lipschitz function $f\\colon\\mathbb R^{d}\\to \\mathbb R$. We show that any universal differentiability set contains a `kernel\' in which the points of differentiability of each Lipschitz function are dense. We further prove that no universal differentiability set may be decomposed as a countable union of relatively closed, non-universal differentiability sets.

[学科分类] 物理化学和理论化学

[关键词] differentiability;Lipschitz functions;universal differentiability set;$\\sigma$-porous setDOI: DOI 10.14712/1213-7243.2015.218AMS Subject Classification: 46G05 46T20 PDF