Inserted: 28 jun 2011
Last Updated: 12 oct 2019
Journal: J. Funct. Anal.
We prove that every acyclic normal one-dimensional real Ambrosio-Kirchheim current in a Polish (i.e. complete separable metric) space can be decomposed in curves, thus generalizing the analogous classical result proven by S. Smirnov in Euclidean space setting. The same assertion is true for every complete metric space under a suitable set-theoretic assumption.
Keywords: currents, metric, decomposition