Inserted: 10 mar 2017
Last Updated: 28 may 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 (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