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 28 May 2017


Published Paper

Inserted: 10 mar 2017
Last Updated: 28 may 2017

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

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 (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 Golab’s semicontinuity theorem.

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


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