Metric spaces of partitions and Caccioppoli partitions

We present a general framework where countable partitions of a measure space (X,M, μ)become elements of a metric space defined by means of a suitable distance function. Aftera detailed study of their metric properties, we consider partitions of Rn with locally finiteinterface area (Caccioppoli partitions). We present some meaningful results (in particular,P-decomposition and regularity) which can form a theoretical basis for the application tovariational problems.