# Metric spaces of partitions, and Caccioppoli partitions

created on 06 Jan 2002
modified by leonardi on 17 Dec 2006

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Published Paper

Inserted: 6 jan 2002
Last Updated: 17 dec 2006

We introduce a general framework where countable partitions of a measure space $(X,\mathcal M,\mu)$ become elements of a metric space defined by means of a suitable distance function. After a detailed study of their metric properties, we consider partitions of $\mathbf R^n$ with locally finite interface area (Caccioppoli partitions). We present some meaningful results (in particular, P-decomposition and regularity) which can form a theoretical basis for the application to variational problems.