Contents 1. Introduction 2 1.1. The Keyfitz and Kranzer system 2 1.2. Bressan's compactness conjecture 3 1.3. Ambrosio's renormalization Theorem 4 1.4. Well–posedness for the Keyfitz and Kranzer system 5 1.5. Renormalization conjecture for nearly incompressible BV fields 6 1.6. Plan of the paper 7 2. Preliminaries 8 2.1. Notation 8 2.2. Measure theory 9 2.3. Approximate continuity and approxima...

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