MEASURE THEORY

A₁ absolutely continuous algebra assertion B₁ Baire set Borel measure Borel set Cartesian product class of sets compact set containing converges a.e. converges in measure decreasing sequence defined denote disjoint union E₁ element empty exists a set extended real valued F₁ F₂ fn(x follows from Theorem function ƒ ƒ and g Haar measure Hausdorff space hereditary o-ring Hint implies inner regular integrable function integrable simple functions intersection Lebesgue measurable locally compact measurable function measurable set measurable subset measurable transformation measure ring measure space measure zero metric space negative o-finite o-ring open set outer measure positive integer positive measure positive number product space Proof prove real line real numbers respect sequence f sequence of sets set function set of positive sets of finite signed measure tion topological group write µ(En