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  "body": "\n## Summary\n\nA set function is countably additive, or σ-additive, if its value on a countable disjoint union is the sum of its values on the pieces.\nCountable additivity is the defining property of measures.\nIt is stronger than finite additivity, and it is what makes limit theorems such as monotone convergence work.\n\n## Explanations\n\n### L1 human\n\nCountable additivity says that sizes add up even when a set is cut into infinitely many pieces, as long as there are only countably many.\nFor example, $[0, 1)$ is the disjoint union of $[1 - 2^{-n+1}, 1 - 2^{-n})$ for $n \\ge 1$, of lengths $1/2, 1/4, 1/8, \\ldots$.\nThese lengths add up to $1$, the length of $[0, 1)$.\nWithout this rule, one could not pass to limits when computing sizes.\n",
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