Lebesgue decomposition theorem
= Lebesgue decomposition theorem
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For sigma-finite measures $\nu$ and $\mu$, there is a unique decomposition $\nu=\nu_{\mathrm{ac}}+\nu_{\mathrm{s}}$ in which $\nu_{\mathrm{ac}}\ll\mu$ and $\nu_{\mathrm{s}}\perp\mu$.