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  "body": "\n## Summary\n\nA set-valued measure assigns to each measurable set a nonempty subset of $\\R^n$, and it is countably additive for the Minkowski sum of sets.\nIt generalises a [[vector measure|PS28BSAJKJ]], which assigns a single vector to each set.\nSet-valued measures arise, for example, as integrals of set-valued functions over measurable sets.\nThey are studied in mathematical economics and in control theory.\n\n## Explanations\n\n### L1 human\n\nAn ordinary measure gives each set one number, its size.\nA set-valued measure gives each set a whole region of possible values.\nFor two disjoint sets, the region of the union consists of all sums of a value from the first region and a value from the second.\nFor example, giving each set $A$ the interval $[0, \\mu(A)]$ for a finite measure $\\mu$ is a set-valued measure on the line.\n",
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