ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Binary cartesian set product
▼ Binary relation
▼ Map
▼ Function
▼ Measure
▼ Real measure
▼ Euclidean real measure
▼ Complex measure
▼ Basic measure
▼ Unsigned basic measure
Definition D2887
Absolutely continuous measure
Formulation 2
Let $\mu, \nu : \mathcal{F} \to [0, \infty]$ each be an D85: Unsigned basic measure.
Then $\nu$ is absolutely continuous with respect to $\mu$ if and only if \begin{equation} \forall \, E \in \mathcal{F} \left( \mu(E) = 0 \quad \implies \quad \nu(E) = 0 \right) \end{equation}
Children
▶ D3567: Measure absolute continuity relation