reference request – Role of the absolute continuity of the divergence of the BV function in the proof of the renormalization property

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

Happily, what is the role of one of the key assumptions of the article: $ mathrm {div} , a $ is absolutely continuous compared to Lebesgue's measure?

Note. A related question is posed in the post-BV function with an absolutely continuous divergence