Differentiability of Lipschitz functions in Lebesgue null sets

• 成果类型: Article
• 署名作者: Preiss, David; Speight, Gareth
• 署名单位: University of Warwick; Scuola Normale Superiore di Pisa
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0520-5
• 发表日期: 2015
• 页码: 517-559
• 关键词: frechet differentiability; Hausdorff Dimension

摘要

We show that if then there exists a Lebesgue null set in containing a point of differentiability of each Lipschitz function ; in combination with the work of others, this completes the investigation of when the classical Rademacher theorem admits a converse. Avoidance of -porous sets, arising as irregular points of Lipschitz functions, plays a key role in the proof.