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  "body": "\n## Summary\n\nThe essential supremum of a measurable function is the smallest number that the function exceeds only on a set of measure zero.\nIt is the supremum that ignores what happens on null sets.\nIt gives the norm of the space $L^\\infty$, and it is the natural bound when functions are only known up to equality almost everywhere.\n\n## Explanations\n\n### L1 human\n\nThe ordinary supremum is the least upper bound of all the values of a function.\nA single wild value at one point can make it huge, even though one point does not matter for integrals.\nThe essential supremum throws away such values when they live on a set of measure zero.\nFor example, let $f(x) = 0$ for $x \\ne 0$ and $f(0) = 100$ on the real line with Lebesgue measure.\nIts supremum is $100$, but its essential supremum is $0$.\n",
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