Vitushkin's Conjecture for Removable Sets

Vitushkin''s conjecture, a special case of Painlevé''s problem, states that a compact subset of the complex plane with finite linear Hausdorff measure is removable for bounded analytic functions if and only if it intersects every rectifiable curve in a set of zero arc length measure.  Chapters 6-8 of this carefully written text present a major recent accomplishment of modern complex analysis, the ...