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Some fine properties of currents and applications to distributional Jacobians
Camillo De Lellis
We study fine properties of currents in the framework of geometric measure theory on metric spaces developed by Ambrosio and Kirchheim in  and we prove a rectifiability criterion for flat currents of finite mass. We apply these tools to study the structure of the dis-tributional Jacobians of functions in the space BnV, defined by Jerrard and Soner in . We define the subspace of special functions of bounded higher variation and we prove a closure theorem.
 Ambrosio L., Kirchheim B. Currents on metric spaces. Mat. Annalen. To appear.  Jerrard L., Soner M. Functions of higher bounded variation. Forthcoming.