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  "body": "\n## Definition\n\nLet $(\\Omega, \\mathcal{F}, P)$ be a [[probability space|0ZYBZ34RT2]].\nAn [[event|00SQGJNRTB]] $E \\in \\mathcal{F}$ happens almost surely if $P(E) = 1$.\nMore generally, a property of outcomes holds almost surely (a.s.) if an event of probability $0$ contains all outcomes where it fails.\n\n## Remarks\n\nThe property need not hold for all outcomes. In this sense, \"almost surely\" is weaker than \"surely\".\nTwo random variables $X$ and $Y$ are equal almost surely if $P(X = Y) = 1$. They then have the same law.\nA countable intersection of events that happen almost surely also happens almost surely.\nIt is the probability form of \"almost everywhere\" in measure theory.\n\n## Explanations\n\n### L1 human\n\nIf you choose a uniform random number in $[0, 1]$, it is almost surely irrational. Rational outcomes are possible, but together they have probability $0$.\nIf you toss a fair coin forever, you get heads at least once almost surely.\n",
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