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  "body": "\n## Summary\n\nAn algebra of sets on a set $X$ is a family of subsets of $X$ that contains $X$.\nIt is closed under complements and finite unions.\nIt is also called a field of sets.\nAlgebras of sets are the natural domain of finitely additive measures.\nThey are also the starting point of Carathéodory's construction of measures.\n\n## Explanations\n\n### L1 human\n\nAn algebra of sets is a family of subsets that is stable under the basic set operations done finitely many times.\nIf two sets are in the family, then so are their union, their intersection and their complements.\nFor example, on the natural numbers, the finite sets together with the sets whose complement is finite form an algebra.\nA σ-algebra asks more: it must also be stable under countable unions.\n",
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