Geometry of Euclidean Sets: Analytical, Stochastic and Hypertopological Aspects : Distributional Geometry

Distributional Geometry
Geometry of Euclidean Sets: Analytical, Stochastic and Hypertopological Aspects

Author : Jean-Charles PINOLI

Publication date: June 10, 2026 | Lire en français

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4. Distributional Geometry

The eleventh general mathematical framework is that of distributional geometry, which applies distribution theory to geometry (in this case, Euclidean geometry).

4.1 Distribution domain and Caccioppoli set

Definition (distribution domain). Let U be a nonempty open set of $ℝ_{2}^{n}$ and X a Borel subset of $ℝ_{2}^{n}$ . The distributational perimeter, or Caccioppoli-de Giorgi perimeter, of X in the open subset U, denoted by

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Distributional Geometry