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  "body": "\n## Summary\n\nBaire functions are the functions obtained from [[continuous functions|0P27W9RW0G]] by taking [[pointwise limits|056FSKG32J]] of sequences, again and again.\nThey are sorted into Baire classes indexed by the countable ordinals.\nClass $0$ is the continuous functions, and class $1$ is the pointwise limits of continuous functions.\nOn $\\R$, the Baire functions are exactly the Borel measurable functions.\nThe classes give a fine measure of how far a function is from being continuous.\n\n## Explanations\n\n### L1 human\n\nPointwise limits of continuous functions need not be continuous.\nFor example, $x^n$ on $[0, 1]$ tends to a function that is $0$ before $1$ and $1$ at $1$.\nSuch limits form Baire class $1$.\nLimits of those can be even rougher, and they form class $2$, and the process continues.\n",
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