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 us 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 ≥ 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.

Rectifiability and Approximate Differentiability of Higher Order for Sets

Santilli M.
2019

Abstract

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 us 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 ≥ 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/176967
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