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  "body": "\n## Summary\n\nA σ-finite measure is a measure for which the whole space is a countable union of sets of finite measure.\nLebesgue measure on $\\R^n$ is the main example.\nMany basic theorems, such as the Fubini–Tonelli theorem and the Radon–Nikodym theorem, assume σ-finiteness.\n\n## Explanations\n\n### L1 human\n\nA σ-finite measure may give the whole space infinite size, but the space can be cut into countably many pieces of finite size.\nThe real line has infinite length, yet it is the union of the intervals $[-n, n]$, each of finite length.\nCounting measure on the real line is not σ-finite: a set of finite counting measure is finite, and countably many finite sets cannot cover the line.\n",
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