Complex vector measure and integral over manifolds with locally finite variations (Q2404749)

In the paper under review, integration of differential forms of type \((n,0)\) on subsets of \(\mathbb C^m\) is studied in a way that extends the well-known integration along locally rectifiable curves. One of the main results is that if \(M\) is an oriented manifold of real dimension \(n\) that is smoothly embedded into \(\mathbb C^m\), then \(M\) has locally finite variations and one has a natural formula for the integrals of \((n,0)\)-forms on \(M\).