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  "body": "\n## Summary\n\nA sublinear function on a real vector space is a real-valued map that is positively homogeneous and subadditive.\nNorms, seminorms and linear functionals are all sublinear.\nSublinear functions are the dominating functions in the [[Hahn–Banach theorem|QB5AE3VYZZ]], and the [[Minkowski functional|PAX9SHDHDW]] of a convex set is a basic example.\n\n## Explanations\n\n### L1 human\n\nA sublinear function behaves like a length that may be lopsided.\nScaling a vector by a positive number scales the value by the same number.\nThe value of a sum is at most the sum of the values, as in the triangle inequality.\nOn the plane, $p(x_1, x_2) = \\max(x_1, x_2)$ is sublinear but is not a norm, because it can be negative.\n",
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