Added facts about vector measures.

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Bokuan Li
2026-03-15 19:30:28 -04:00
parent 2e160500cc
commit b5126e965b
16 changed files with 568 additions and 41 deletions

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src/measure/vector/ac.tex Normal file
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\section{Absolutely Continuous}
\label{section:absolutely-continuous-measure}
\begin{definition}[Absolutely Continuous]
\label{definition:absolutely-continuous}
Let $(X, \cm)$ be a measurable space and $\mu, \nu$ be signed/vector measures on $X$, then $\nu$ is \textbf{absolutely continuous} with respect to $\mu$, denoted $\nu \ll \mu$, if every $\mu$-null set is $\nu$-null.
\end{definition}