# Role of absolute continuity of divergence of BV function in proof of renormalization property

In the paper http://cvgmt.sns.it/paper/436/, the author proves the renormalization property for the flow generated by a vector field $$a(t,\cdot) \in BV(\mathbb{R}^N; \mathbb{R}^N)$$.

Heuristically, what is the role of one of the key assumptions of the paper: that $$\mathrm{div}\, a$$ is absolutely continuous with respect to the Lebesgue measure?

Note. A related question is asked in the post BV function with absolutely continuous divergence