Some generalizations of the concept of length
type: Item
instance of: scholarly article
title: Some generalizations of the concept of length
zbMATH Open document ID: 1029.31001
DOI: 10.1023/A:1012911901646
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: The paper is devoted to two numerical characteristics of a nonrectifiable are \(\gamma\subset\mathbb{C}\) generalizing the notion of length. Geometrically, this notion can naturally be generalized as the least upper bound of the sums \(\sum\varphi(a_j)\), where \(a_j\) are the lengths of segments of a polygonal line inscribed in the curve \(\gamma\) and \(\varphi\) is a given function. The author provides conditions under which the generalized geometric rectifiability of a curve \(\gamma\) implies its generalized analytic rectifiability.
Mathematics Subject Classification ID: 31A15
zbMATH DE Number: 1927823
zbMATH Keywords: nonrectifiable are
zbMATH Keywords: generalized geometric rectifiability
zbMATH Keywords: generalized analytic rectifiability
author: Boris A. Kats
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: a:1012911901646
OpenAlex ID: W59802651
description: scientific article; zbMATH DE number 1927823