Additive subsets have been introduced in the framework of discrete tomography with the underlying notion of x-rays. This notion can be defined from two different ways. We provide in the paper extensions of the two definitions and a proof of their equivalence in a framework where x-rays are replaced by any subsets. It results a pair of dual definitions of additivity cleared out from dispensable assumptions and a proof of their equivalence reduced to a separation theorem.
展开▼
