Geometric Measure Theory : The fractional β-dimensional Hausdorff measure

The fractional β-dimensional Hausdorff measure
Geometric Measure Theory

Author : Jean-Charles PINOLI

Publication date: April 10, 2016 | Lire en français

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16. The fractional β-dimensional Hausdorff measure

16.1 Definition

Definition (β-dimensional Hausdorff measure) (1918). The (exterior) β-dimensional Hausdorff measure, denoted $μ_{H}_{n}^{β}$ , for a real number β ∊ [0, n], of any subset X of $ℝ^{n}$ is defined by (

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The fractional β-dimensional Hausdorff measure

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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...

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The fractional β-dimensional Hausdorff measure Geometric Measure Theory

16. The fractional β-dimensional Hausdorff measure

16.1 Definition

Bibliography

The fractional β-dimensional Hausdorff measure
Geometric Measure Theory