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  "body": "\n## Summary\n\nA measurable function is a map between [[measurable spaces|N4KDT83V3S]] under which the preimage of every measurable set is measurable.\nThese are the functions that one can integrate in Lebesgue's theory, and in probability they are the random variables.\nSums, products, limits and suprema of sequences of real measurable functions are again measurable.\n\n## Explanations\n\n### L1 human\n\nTo integrate a function, one needs to know how big the set is where the function lies in a given range.\nA measurable function is one for which all these sets can be measured.\nFor example, on the real line, every continuous function is measurable, and so is the function that is $1$ on the rational numbers and $0$ elsewhere.\nMeasurable functions are the analogue for measure theory of continuous functions in topology.\n",
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