The dirac outer measure.

Given any function m assigning measures to sets satisying m ∅ = 0, there is a unique maximal outer measure μ satisfying μ s ≤ m s for all s : set α.

Given an outer measure μ, the Caratheodory measurable space is defined such that s is measurable if ∀t, μ t = μ (t ∩ s) + μ (t \ s).