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  "body": "\n## Summary\n\nA subset of a topological space has the Baire property if it differs from an [[open set|02BH3MCBQB]] by a [[meagre set|0XGCZ4GDZ6]].\nIt is the topological analogue of Lebesgue measurability, with meagre sets in the role of null sets.\nThe sets with the Baire property form a sigma-algebra that contains all Borel sets, and in a Polish space it also contains all [[analytic sets|3RWWZYPAFV]].\nUnder the axiom of choice there are sets of reals without the Baire property.\n\n## Explanations\n\n### L1 human\n\nMeagre sets are the \"topologically small\" sets, such as countable sets of reals or the Cantor set.\nA set has the Baire property when, after ignoring a small set of errors, it looks like an open set.\nFor example, the closed interval $[0, 1]$ differs from the open interval $(0, 1)$ only by the two points $0$ and $1$, and a finite set is meagre.\nSo $[0, 1]$ has the Baire property.\nSets with this property behave well in arguments that use the [[Baire category theorem|0A7KGAYHGV]].\n",
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