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  "body": "\n## Summary\n\nPacking measure gives the $s$-dimensional size of a set in a [[metric space|0VKD1TP7F3]].\nIt packs disjoint small balls centred in the set, instead of covering the set.\nIt is a dual of [[Hausdorff measure|Q1TGZK8RN6]], which uses covers.\nIt leads to the packing dimension, which is at least the Hausdorff dimension, and the two can differ for irregular fractals.\n\n## Explanations\n\n### L1 human\n\nHausdorff measure asks for the most economical way to cover a set by small pieces.\nPacking measure asks the opposite question: how much room can one fill with disjoint small balls whose centres lie in the set.\nEach ball counts by its diameter to the power $s$.\nFor a line segment of length $1$ and $s = 1$, the best packings fill the segment almost completely, and the packing measure is $1$.\n",
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