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11. Minkowski's contents
It is important to "measure" non-zero co-dimensional subsets of , i.e. subsets of dimension strictly less than n (e.g. a curve in dimension 2 or 3, and a surface in dimension 3). Previously introduced measures are inappropriate (e.g. the Peano-Jordan content or the Lebesgue measure), or difficult or impossible to calculate (e.g. the Hausdorff measure). A useful notion is provided by Minkowski contents.
11.1 Minkowski's m-dimensional content
Definition (m-dimensional Minkowski content). The m-dimensional Minkowski content of a subset X of
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