Inserted: 10 mar 2017
Last Updated: 4 oct 2017
Journal: Nonlinear Analysis
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