Metric spaces of partitions and Caccioppoli partitions
Gian Paolo Leonardi, Italo Tamanini · 2002
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. After a detailed study of their metric properties, we consider partitions of Rn 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. 1