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  "body": "\n## Summary\n\nThe Minkowski content measures the $m$-dimensional size of a subset of $\\R^n$ through the volume of its thin neighbourhoods.\nOne thickens the set by $r$, takes the [[Lebesgue measure|2Z2QVWZ262]] of the result, and divides by the volume of an $(n-m)$-dimensional ball of radius $r$.\nFor nice sets it gives length, area and volume, and for rough sets it is linked to the box-counting dimension.\n\n## Explanations\n\n### L1 human\n\nTo find the length of a curve in the plane, paint a thin band of width $2r$ around it and measure the area of the band.\nThe area is close to $2r$ times the length, so dividing by $2r$ recovers the length as $r$ shrinks.\nFor a segment of length $L$, the band is a rectangle of area $2rL$ with two half-discs at the ends, and the ratio tends to $L$.\nThe same idea measures surfaces in space through thin shells.\n",
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