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 (

You do not have access to this resource.

Exclusive to subscribers. 97% yet to be discovered!

You do not have access to this resource. Click here to request your free trial access!

Already subscribed? Log in!

Ongoing reading
The fractional β-dimensional Hausdorff measure

Previous
page Gross and Favard m-dimensional measurements

Lebesgue and Lebesgue-Hausdorff densities

Article included in this offer

"Mathematics"

( 165 articles )

Complete knowledge base

Updated and enriched with articles validated by our scientific committees

Services

A set of exclusive tools to complement the resources

View offer details

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...

You do not have access to this resource.

Exclusive to subscribers. 97% yet to be discovered!

You do not have access to this resource. Click here to request your free trial access!

Already subscribed? Log in!