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\end{proof}
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\end{proof}
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\begin{definition}[Hermitian]
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\label{definition:hermitian-functional}
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Let $E$ be a vector space over $\real$, $*: \complex(E) \to \complex(E)$ be the canonical complex conjugation map, and $\phi \in \hom(\complex(E); \complex)$, then the following are equivalent:
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\begin{enumerate}
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\item $\phi|_E \in \hom(E; \real)$.
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\item For each $x \in E$, $\dpn{x, \phi}{\complex(E)} = \ol{\dpn{x^*, \phi}{\complex(E)}}$.
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\end{enumerate}
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If the above holds, then $\phi$ is \textbf{Hermitian}.
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\end{definition}
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@@ -16,7 +16,7 @@
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\end{definition}
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\end{definition}
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\begin{example}
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\begin{example}
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Let $X$ be a LCH space, $\mu$ be a Radon measure, and $\mathcal{K}$ be the collection of compact subsets of $X$, then $\mathcal{K}$ is a scaffold for $\mu$.
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Let $X$ be a LCH space, $\mu$ be a semifinite Radon measure, and $\mathcal{K}$ be the collection of compact subsets of $X$, then $\mathcal{K}$ is a scaffold for $\mu$.
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\end{example}
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\end{example}
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% Omitted
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% Omitted
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@@ -12,7 +12,7 @@
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If $A$ and $B$ are unital, then $\phi$ is \textbf{unital} if:
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If $A$ and $B$ are unital, then $\phi$ is \textbf{unital} if:
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\begin{enumerate}
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\begin{enumerate}
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\item[(U)] $\phi(1_A) = \one_B$.
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\item[(U)] $\phi(1_A) = 1_B$.
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\end{enumerate}
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\end{enumerate}
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\end{definition}
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\end{definition}
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