The paper is devoted to a new proof of the compactness theorem in SBV, originally proved by L. Ambrosio by an integralgeometric argument [Boll. Unione Mat. Ital., VII Ser. B 3, No. 4, 857-881 (1989; Zbl 0767.49001)]. As in L. Ambrosio [Calc. Var. Partial Differ. Equ. 3, No. 1, 127-137 (1995; Zbl 0837.49011)], where a similar idea was used under more restrictive assumptions, the central point of the new proof is the analysis of the distributional derivative , where and is a Lipschitz function. Given an increasing function satisfying as and an open set , it turns out that and if and only if
for some absolutely continuous measure . Here denotes the collection of Lipschitz and continuously differentiable functions such that
Moreover, if (1) holds, then has the approximate differential of as density.