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  "body": "\n## Summary\n\nA property of the points of a measure space holds almost everywhere if the points where it fails lie in a set of measure zero.\nMost statements about integrals and measurable functions only hold, and only need to hold, almost everywhere.\nIn probability theory the same notion is called almost surely.\n\n## Explanations\n\n### L1 human\n\n\"Almost everywhere\" means \"everywhere except on a negligible set\".\nThe function that is $1$ at rational numbers and $0$ elsewhere is $0$ almost everywhere on the real line.\nThe rational numbers form a countable set, which has length zero.\nTwo functions that agree almost everywhere have the same integral, so measure theory treats them as the same.\n",
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