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  "body": "\n## Summary\n\nA Borel measure on a topological space is a [[measure|PR11BZQQPG]] defined on the [[Borel sets|0WQXY32Q8D]], the sets generated by the open sets.\nIt is the natural kind of measure on spaces such as $\\R^n$, manifolds and topological groups, where open sets and continuous functions are given.\nEvery continuous real function is measurable for a Borel measure.\nSome authors also require a Borel measure to be finite on compact sets.\n\n## Explanations\n\n### L1 human\n\nOn a space with a notion of open sets, the Borel sets are all the sets one can build from open sets by complements and countable unions.\nA Borel measure assigns a size to each of these sets.\nLength on the real line, area in the plane and the point mass at a point are Borel measures.\nThey give sizes to intervals, open discs, closed sets, countable sets and much more.\n",
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