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  "body": "\n## Summary\n\nA regular measure on a topological space is a Borel measure that is both [[inner regular|28E5Q5BM69]] and [[outer regular|33C1KEK3SC]].\nEach measurable set can then be approximated from inside by compact sets and from outside by open sets.\nRegularity ties the measure to the topology and allows integrable functions to be approximated by continuous functions.\nConventions differ between authors: some approximate from inside by closed sets rather than compact sets.\n\n## Explanations\n\n### L1 human\n\nFor a regular measure, every set of finite measure can be squeezed between a compact set inside it and an open set around it.\nThe measure between the two can be made as small as one likes.\nLength on the real line is the main example.\nFor the interval $[0, 1)$, the compact sets $[0, 1 - \\varepsilon]$ inside and the open sets $(-\\varepsilon, 1)$ outside have lengths as close to $1$ as one likes.\n",
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