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@@ -52,7 +52,7 @@
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\begin{enumerate}
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\item[(a)] $f_n \to f$ strongly pointwise.
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\item[(b)] There exists $g \in L^1(X) \cap L^+(X)$ such that $\norm{f_n}_E \le g$ for all $n \in \natp$.
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\end\{enumerate\}
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\end{enumerate}
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then $\int f d\mu = \limv{n}\int f_n d\mu$.
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@@ -77,7 +77,7 @@
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\begin{enumerate}
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\item For any $x \in E$ and $A \in \cm$, $I_\lambda(x \cdot \one_A) = x \mu(A)$.
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\item For any $f \in L^1(X, |\mu|; E)$, $\normn{I_\lambda f}_{G} \le \norm{\lambda}_{L^2(E, F; G)} \cdot \norm{f}_{L^1(X, |\mu|; E)}$.
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\end\{enumerate\}
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\end{enumerate}
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For any $f \in L^1(X; E)$, $I_\lambda f = \int \lambda(f, d\mu)$ is the \textbf{Bochner integral} of $f$ with respect to $\mu$ and $\lambda$.
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@@ -98,7 +98,7 @@
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\begin{enumerate}
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\item[(a)] $f_n \to f$ strongly pointwise.
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\item[(b)] There exists $g \in L^1(X) \cap L^+(X)$ such that $\norm{f_n}_E \le g$ for all $n \in \natp$.
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\end\{enumerate\}
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\end{enumerate}
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then $\int \lambda(f , d\mu) = \limv{n}\int \lambda(f_n, d\mu)$.
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