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Article | REF: AF109 V1

Bounded Variation Functions

Author: Jean-Charles PINOLI

Publication date: May 10, 2025 | Lire en français

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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 ℝn and B a Borellian subset of ℝn . The perimeter of B in U, denoted Per(B,U), is the total variation of the indicator function 1 ...

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