On the structure of continua with finite length and Gołąb's semicontinuity theorem. (April 2017)

• Record Type: Journal Article
• Authors: Alberti, Giovanni; Ottolini, Martino
• Is Part Of: Nonlinear analysis. Volume 153(2017)
• Page Start: 35
• Page End: 55
• Publication Date: 2017-04
• Subjects: 28A75 -- 54F50 -- 26A45 -- 49J45 -- 49Q20; Continua with finite length -- Hausdorff measure -- Gołąb's semicontinuity theorem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.10.012
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The main results in this note concern the characterization of the length of continua 1 (Theorem 2.5 ) and the parametrization of continua with finite length (Theorem 4.4 ). Using these results we give two independent and relatively elementary proofs of Gołąb's semicontinuity theorem.