Oxford? comma.
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\begin{theorem}[Lebesgue-Radon-Nikodym]
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\label{theorem:lebesgue-radon-nikodym}
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Let $(X, \cm)$ be a measurable space, $\mu$ be a $\sigma$-finite positive measure on $(X, \cm)$, $H$ be a Hilbert space over $K \in \RC$ and $\nu: \cm \to H$ be a finite vector measure, then there exists a unique pair of finite vector measures $\nu_a, \nu_s: \cm \to H$ such that:
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Let $(X, \cm)$ be a measurable space, $\mu$ be a $\sigma$-finite positive measure on $(X, \cm)$, $H$ be a Hilbert space over $K \in \RC$, and $\nu: \cm \to H$ be a finite vector measure, then there exists a unique pair of finite vector measures $\nu_a, \nu_s: \cm \to H$ such that:
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\begin{enumerate}
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\item $\nu = \nu_a + \nu_s$.
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\item $\nu_a$ is absolutely continuous with respect to $\mu$.
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