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  "body": "\n## Summary\n\nA Riesz space, or vector lattice, is an [[ordered vector space|HHMS3WH9T7]] whose order is a [[lattice|WH4SFAACAS]].\nIt is at the same time a real vector space and a [[lattice-ordered group|J0DHYQ0MDE]].\nSpaces of real functions with the pointwise order, such as spaces of continuous functions and $L^p$ spaces, are Riesz spaces.\nRiesz spaces are the setting for positive operators and for [[Banach lattices|HDJ1GKG0NA]] in functional analysis.\n\n## Explanations\n\n### L1 human\n\nIn the space of real functions on an interval, you can add functions, scale them, and compare them point by point.\nFor two functions you can also take their pointwise maximum and minimum.\nA Riesz space is a vector space with an order where these maxima and minima always exist and behave well with addition and scaling.\nFor instance, the absolute value $\\abs{f} = \\max(f, -f)$ of a function makes sense in any Riesz space.\n",
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