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: #m/def/measure

𝜈 ≪ 𝜇 ⟺ (\forall 𝐴 \in Σ) [𝜇 (𝐴) = 0 ⟹ 𝜈 (𝐴) = 0]

Properties

Radon-Nikodym theorem

#state/tidy | #lang/en | #SemBr