Inserted: 23 dec 2019
Last Updated: 23 dec 2019
We consider the structure of divergence-free vector measures on the plane. We show that such measures can be decomposed into measures induced by closed simple curves. We also discuss similar decompositions for some measures with nonzero divergence. As an application we generalize certain rigidity properties of divergence-free vector fields to vector-valued measures.
Keywords: superposition principle, Vector-valued measures, Divergence-free measures