diff --git a/src/measure/vector/rn.tex b/src/measure/vector/rn.tex index 6473e27..566b9a9 100644 --- a/src/measure/vector/rn.tex +++ b/src/measure/vector/rn.tex @@ -37,7 +37,7 @@ then \begin{enumerate} - \item By definition, $\nu = \nu_a + \nu_s$. + \item Since $X = A \sqcup B$, $\nu = \nu_a + \nu_s$. \item Let $E \in \cm$ with $\mu(E) = 0$, then $(1 - g)|_E = 0$ $\lambda$-almost everywhere. Thus $E \subset B$ modulo a $\lambda$-null set, and \[ \nu_a(E) = \nu(E \cap A) \le \lambda(A \cap B) = 0