集合的可求正性与高阶近似可微性
Rectifiability and approximate differentiability of higher order for sets
摘要：
本文的主要目标是发展一个概念的近似微分高阶子集的欧几里得空间，允许表征高阶可求长集，扩展某种众所周知的事实的功能。我们强调，对于欧几里得空间的每个子集$ A $和每个整数$ k \geq 2 $，我们引入了$ A $的$ k $阶近似微分，并证明了它是一个Borel映射，其定义域是一个（可能空的）博雷尔集.这一概念有助于在应用中处理高阶可求长集。
英文摘要：
The main goal of this paper is to develop a concept of approximate differentiability of higher order for subsets of the Euclidean space that allows to characterize higher order rectifiable sets, extending somehow well known facts for functions. We emphasize that for every subset $ A $ of the Euclidean space and for every integer $ k \geq 2 $ we introduce the approximate differential of order $ k $ of $ A $ and we prove it is a Borel map whose domain is a (possibly empty) Borel set. This concept could be helpful to deal with higher order rectifiable sets in applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
