Geometric Measure Theory

Parallel sets
Geometric Measure Theory

Author : Jean-Charles PINOLI

Publication date: April 10, 2016 | Lire en français

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10. Parallel sets

10.1 Parallel interior and exterior assemblies

Minkowski's addition ⊕ (1903) and Minkowski's subtraction ⊖ provide the means of introducing inner and outer parallel subsets of a subset X of $ℝ^{n}$ .

Definition (inner and outer parallel sets). The inner and outer parallel subsets of a subset X of $ℝ^{n}$ are noted $X_{r}^{+}$ and

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Parallel sets

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page Hausdorff's m-dimensional measurement

Minkowski's contents

Bibliography

(1) - ALBERTI (G.) - Geometric measure theory. - Encyclopedia of Mathematical Physics, Vol. 2, pp. 520-527 (J.-P. Françoise et al, eds), Elsevier (2006).
(2) - AMBROSIO (L.), CAPASSO (V.), VILLA (E.) - On the approximation of mean densities of random closed sets. - Bernoulli,...

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Parallel sets Geometric Measure Theory

10. Parallel sets

10.1 Parallel interior and exterior assemblies

Bibliography

Parallel sets
Geometric Measure Theory