Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590800 | Journal of Functional Analysis | 2013 | 27 Pages |
Abstract
We prove that every one-dimensional real Ambrosio–Kirchheim normal current in a Polish (i.e. complete separable metric) space can be naturally represented as an integral of simpler currents associated to Lipschitz curves. As a consequence a representation of every such current with zero boundary (i.e. a cycle) as an integral of so-called elementary solenoids (which are, very roughly speaking, more or less the same as asymptotic cycles introduced by S. Schwartzman) is obtained. The latter result on cycles is in fact a generalization of the analogous result proven by S. Smirnov for classical Whitney currents in a Euclidean space. The same results are true for every complete metric space under suitable set-theoretic assumptions.
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