\(C^{\gamma}\)-property and approximately differentiable functions
type: Item
instance of: scholarly article
title: \(C^{\gamma}\)-property and approximately differentiable functions
zbMATH Open document ID: 0689.26008
DOI: 10.1007/BF01158424
author: N. M. Isakov
published in: Mathematical Notes
publication date: 1988-01-01T00:00:00Z
review text: We say that a transformation \(f\) from \(R^n\) to \(R^m\) has \(C^{\gamma}\)-property if for every ball \(B\) in \(R^n\) and for each \(\varepsilon >0\) there exists a compact set \(K\subset B\) and the transformation \(g\in \mathrm{lip}^{\gamma}(R^n,R^m)\) such that \(mK >mB- \varepsilon\) and \(f| K=g| K\) (here \(m\) is the \(n\)-dimensional Lebesgue measure). The paper gives three characterizations of the property \(C^{\gamma}\). The main result can be considered as a generalization of theorems of Khintchine, Bernstein and Whitney [see, for example \textit{H. Federer}, ``Geometric measure theory.'' [Berlin etc.: Springer Verlag (1969; Zbl 0176.00801), p. 228].
Mathematics Subject Classification ID: 26B05
Mathematics Subject Classification ID: 26B40
zbMATH DE Number: 4129125
zbMATH Keywords: approximately differentiable functions
zbMATH Keywords: jets
reviewed by: Władysław Wilczyński
MaRDI profile type: Publication
cites work: Q5607484
cites work: On a global property of approximately differentiable functions
cites work: Q5565773
full work available at URL: https://doi.org/10.1007/bf01158424
OpenAlex ID: W4233004783
description: scientific article; zbMATH DE number 4129125