Geometry of Euclidean Sets: Vectorial, Topological and Metric Aspects : Geometric Measure Theory I: Measures

Geometric Measure Theory I: Measures
Geometry of Euclidean Sets: Vectorial, Topological and Metric Aspects

Author : Jean-Charles PINOLI

Publication date: May 10, 2026 | Lire en français

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10. Geometric Measure Theory I: Measures

The eighth general mathematical framework is that of geometric measure theory, which deals with the application of measure theory to geometry.

10.1 Functional

A functional, denoted generically by F, is a mapping defined on a class of subsets of Euclidean space $ℝ_{2}^{n}$ (e.g., the class of all nonempty compact subsets under the Euclidean topology) and with numerical values (i.e., in $ℕ$ , $ℤ$ or $ℝ$ ; often

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Geometric Measure Theory I: Measures