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  "body": "\n## Summary\n\nA strongly measurable function is a function from a measurable space to a Banach space that is a pointwise limit of simple measurable functions.\nIt is the right notion of measurability for functions with values in an infinite-dimensional space.\nThe Bochner integral is built for strongly measurable functions, and the Pettis measurability theorem describes them through linear functionals.\n\n## Explanations\n\n### L1 human\n\nA simple function takes only finitely many values, each on a measurable piece of the space.\nA strongly measurable function is one that such simple functions can approximate as closely as one wants at every point.\nFor real-valued functions this is the same as ordinary measurability.\nFor example, a continuous function $f \\colon [0, 1] \\to E$ into a Banach space $E$ is strongly measurable.\nTo see it, cut $[0, 1]$ into $n$ intervals and take on each interval the value of $f$ at its left end.\nThese step functions converge to $f$ at every point as $n$ grows.\n",
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