Editing Analytic capacity (section)

==Removable sets and Painlevé's problem==
The compact set ''K'' is called '''removable''' if, whenever Ω is an open set containing ''K'', every function which is bounded and holomorphic on the set Ω&nbsp;\&nbsp;''K'' has an analytic extension to all of Ω. By [[Removable singularity#Riemann's theorem|Riemann's theorem for removable singularities]], every [[singleton (mathematics)|singleton]] is removable. This motivated Painlevé to pose a more general question in 1880: "Which subsets of '''C''' are removable?"

It is easy to see that ''K'' is removable if and only if ''γ''(''K'') = 0. However, analytic capacity is a purely complex-analytic concept, and much more work needs to be done in order to obtain a more geometric characterization.