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.
Metric spaces of partitions and Caccioppoli partitions / Leonardi, Gian Paolo; Tamanini, I.. - In: ADVANCES IN MATHEMATICAL SCIENCES AND APPLICATIONS. - ISSN 1343-4373. - STAMPA. - 12:2(2002), pp. 725-753.
Metric spaces of partitions and Caccioppoli partitions
LEONARDI, Gian Paolo;
2002
Abstract
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.
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