Calculus of Variations and Geometric Measure Theory
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G. Alberti - M. Ottolini

On the structure of continua with finite length and Golab's semicontinuity theorem

created by alberti on 10 Mar 2017
modified on 04 Oct 2017


Published Paper

Inserted: 10 mar 2017
Last Updated: 4 oct 2017

Journal: Nonlinear Analysis
Volume: 153
Pages: 35-55
Year: 2017
Doi: 10.1016/

ArXiv: 1705.09941 PDF

The postprint version of the pdf file is closest to the published paper; the revised version contains a few corrections and improves Proposition 2.8.


The main results in this note concern the characterization of the length of continua 1 (Theorems 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 Golab's semicontinuity theorem.

Keywords: Hausdorff measure, continua with finite length, Golab’s semicontinuity theorem


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