Radon–Nikodym theorem

In mathematics, the Radon–Nikodym theorem is a result in measure theory which states that, given a measurable space ${\displaystyle (X,\Sigma )}$, if a σ-finite measure ${\displaystyle \nu }$ on ${\displaystyle (X,\Sigma )}$ is absolutely continuous with respect to a σ-finite measure μ on ${\displaystyle (X,\Sigma )}$, then there is a measurable function ${\displaystyle f:X\rightarrow [0,\infty )}$, such that for any measurable subset ${\displaystyle A\subset X}$,

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