Fixed typo in Lebesgue lemma.
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@@ -25,7 +25,7 @@
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\label{lemma:lebesgue-non-negative-strict}
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\label{lemma:lebesgue-non-negative-strict}
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Let $(X, \cm, \mu)$ be a measure space and $f \in \mathcal{L}^+(X, \cm)$.
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Let $(X, \cm, \mu)$ be a measure space and $f \in \mathcal{L}^+(X, \cm)$.
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\begin{enumerate}
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\begin{enumerate}
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\item For each $\phi \in \Sigma^+(X, \cm)$, denote $\phi \le_u f$ if there exists $\delta > 0$ such that $\phi + \delta \ge f$ on $\bracs{\phi > 0}$, then
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\item For each $\phi \in \Sigma^+(X, \cm)$, denote $\phi \le_u f$ if there exists $\delta > 0$ such that $\phi + \delta \le f$ on $\bracs{\phi > 0}$, then
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\[
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\[
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\int f d\mu = \sup\bracs{\int \phi d\mu \bigg | \phi \in \Sigma^+(X, \cm), \phi \le_u f}
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\int f d\mu = \sup\bracs{\int \phi d\mu \bigg | \phi \in \Sigma^+(X, \cm), \phi \le_u f}
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\]
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\]
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