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  "body": "\n## Summary\n\nIn set theory, a **normal measure** is a measure on a measurable cardinal $\\kappa$ such that the equivalence class of the identity function on $\\kappa$ maps to $\\kappa$ itself in the ultrapower construction. Equivalently, a measure $\\mu$ on $\\kappa$ is normal iff whenever $f:\\kappa\\to\\kappa$ is such that $f(\\alpha)\u003c\\alpha$ for $\\mu$-many $\\alpha\u003c\\kappa$, then there is a $\\beta\u003c\\kappa$ such that $f(\\alpha)=\\beta$ for $\\mu$-many $\\alpha\u003c\\kappa$. (Here, \"$\\mu$-many\" means that the set of elements of $\\kappa$ where the property holds is a member of the ultrafilter, i.e. has measure 1 in $\\mu$.) Also equivalent, the ultrafilter (set of sets with measure 1) is closed under diagonal intersection.\n",
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