A new Fubini-like criterion for Lebesgue null sets and its relation to Nikodym sets

发布时间：2020-12-10 作者：浏览次数：

Speaker:	Thierry De Pauw	DateTime:	2020年12月14日(周一)下午15:00-16:00
Brief Introduction to Speaker: Thierry De Pauw，华东师范大学教授。		Place:	六号楼二楼报告厅
Abstract:I will review part of the history of differentiation bases for various Lebesgue spaces, starting with the classical Lebesgue density theorem for summable functions, discussing the role of the Vitali covering theorem and how it generalises to averaging with respect to sets of controlled eccentricity. Vitali’s covering theorem does not generalise to the basis of rectangle parallel to the axes (Bohr) yet Lebesgue density theorem generalises to this basis for bounded function (Saks). I will then state various open questions, review the Nikodym set and how it pertains to a conjecture of Zygmund, and I will review the coarea formula due to Federer. Finally I will state and sketch the proof of a partial result that I obtained recently and pertains to this conjecture of Zygmund.