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  "body": "\n## Summary\n\nThe Lebesgue integral assigns a number to each integrable function on a measure space.\nIt is built from simple functions, then non-negative functions, then general functions split into positive and negative parts.\nIt extends the Riemann integral to many more functions and to any measure space.\nIts great strength is the convergence theorems, which let one exchange limits and integrals under mild conditions.\n\n## Explanations\n\n### L1 human\n\nThe Riemann integral cuts the horizontal axis into small pieces.\nThe Lebesgue integral cuts the vertical axis instead: for each range of values it asks how large the set of points with those values is.\nThis handles functions that jump around wildly.\nFor example, the indicator function of the rationals on $[0, 1]$ has no Riemann integral.\nIts Lebesgue integral is $0$, because the rationals form a set of measure zero.\n",
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