Measures A (set) function μ : K → [0,∞], with ∅ ∈ K ⊂ 2 and μ(∅) = 0 is called additive or finitely additive if A,B ∈ K, with A ∪ B ∈ K and A ∩ B = ∅ imply μ(A ∪ B) = μ(A) + μ(B). Similarly, μ is called σ-additive or countably additive if Ai ∈ K, with ⋃∞ i=1 Ai = A ∈ K and Ai ∩ Aj = ∅ for i 6= j imply μ(A) = ∑∞ i=1 μ(Ai). It is clear that if μ is σ-additive then μ is also additive, but the conv...
