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## Flows of measures induced by vector fields

Proceedings of the Royal Society of Edinburgh: Section A. 2018. Vol. 148. No. 4. P. 773-818.
Stepanov E., Paolini E.

We show that for a large class of measurable vector fields in the sense of N. Weaver (i.e. derivations over the algebra of Lipschitz functions), the notion of a flow of the given positive Borel measure similar to the classical one generated by a smooth vector field (in a space with smooth structure) may be defined in a reasonable way, so that the measure flows along'' the appropriately understood integral curves of the given vector field and the classical continuity equation is satisfied in the weak sense.