Measure theory MOC

Dominating measure

Given two measures 𝜇,𝜈 on a measurable space (𝑋,Σ) we say 𝜇 dominates 𝜈 or 𝜈 is absolutely continuous with respect to 𝜈, written 𝜈 ≪𝜇, iff the following holds: measure

𝜈≪𝜇⟺(∀𝐴∈Σ)[𝜇(𝐴)=0⟹𝜈(𝐴)=0]

Properties

• Radon-Nikodym theorem

---

tidy | en | SemBr