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

In the article, 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