Editing Meagre set (section)

==Erdos–Sierpinski duality==
Many arguments about meagre sets also apply to [[null set|null sets]], i.e. sets of Lebesgue measure 0. The Erdos–Sierpinski duality theorem states that if the [[continuum hypothesis]] holds, there is an [[Involution_(mathematics)|involution]] from reals to reals where the image of a null set of reals is a meagre set, and vice versa.<ref>{{Cite arXiv|last=Quintanilla|first=M.|eprint=2206.10754|title=The real numbers in inner models of set theory|date=2022|class=math.LO }} (p.25)</ref> In fact, the image of a set of reals under the map is null if and only if the original set was meagre, and vice versa.<ref>S. Saito, [https://www.artsci.kyushu-u.ac.jp/~ssaito/eng/maths/duality.pdf The Erdos-Sierpinski Duality Theorem], notes. Accessed 18 January 2023.</ref>