9. Caccioppoli sets
The notion of the Caccioppoli set was introduced in 1927-28 by the Italian mathematician R. Caccioppoli (1904-1959), and further developed in 1952-1958 by the Italian mathematician E. de Giorgi (1928-1996). This notion forms the basis of the modern theory of perimeters.
9.1 Definition
Definition (scope) (Caccioppoli, 1927). Let U be a nonempty open of and B a Borellian subset of . The perimeter of B in U, denoted Per(B,U), is the total variation of the indicator function 1B of B in U :
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Caccioppoli sets
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