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  "body": "\n## Definition\n\nA *measure space* is a triple $(X, \\Sigma, \\mu)$, where $(X, \\Sigma)$ is a [[measurable space|N4KDT83V3S]] and $\\mu$ is a [[measure|PR11BZQQPG]] on $(X, \\Sigma)$.\n\n## Remarks\n\nLet $X = \\set{1, \\ldots, 6}$, let $\\Sigma$ be the power set of $X$, and let $\\mu(A) = \\abs{A} / 6$.\nThen $\\Sigma$ is a σ-algebra and $\\mu$ is a measure, since the number of elements is additive over disjoint sets, so $(X, \\Sigma, \\mu)$ is a measure space.\nOn $\\N$, let $\\mathcal{A}$ be the family of finite sets and of sets with finite complement, and let $\\mu(A) = \\abs{A}$ for finite $A$ and $\\mu(A) = \\infty$ otherwise.\nThen $(\\N, \\mathcal{A}, \\mu)$ is not a measure space, since $\\mathcal{A}$ is not a σ-algebra: it does not contain the set of even numbers.\nA measure space with $\\mu(X) = 1$ is a [[probability space|0NFPJVJJHX]].\n",
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