Example image of eyePlorer eyePlorer map for 'Outer measure': Extended real number line Function (mathematics) Mathematics Measure (mathematics) Set (mathematics) Constantin Carathéodory Sigma additivity Carathéodory's extension theorem Felix Hausdorff Hausdorff dimension Invariant (mathematics) Set theory Disjoint sets Sequence Non-measurable set Empty set Null set Monotonic function Subadditivity If and only if Complete measure Sigma-algebra Integral Lebesgue measure Metric outer measure Metric space Borel set Infimum Hausdorff measure Borel regular measure Bernstein set Carathéodory's criterion Ham sandwich theorem Littlewood's three principles of real analysis Luzin N property List of theorems Pre-measure Inner measure Lebesgue–Stieltjes integration Carathéodory's theorem Standard probability space