11. Geometric Measure Theory II: Minkowski's Concepts
It is important to “measure” subsets of of nonzero codimension, that is, subsets of dimension strictly less than n (e.g., a curve in 2 or 3 dimensions, and a surface in 3 dimensions). The measures introduced earlier are inappropriate (e.g., the Lebesgue measure ), or difficult, if not impossible, to compute (e.g., the Hausdorff measure). A useful concept is provided by Minkowski's contents.
11.1 – -dimensional Minkowski 1-dimensional exterior content
Definition ( – -1-dimensional Minkowski outer content)....
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Geometric Measure Theory II: Minkowski's Concepts
Geometric Measure Theory III: Geometric Densities
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