an intutive explanation for the radon nikodym derivative

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Can anyone please assist with an intuitive explanation for the Radon-Nikodym derivative in application to defining a set of probability measures for set(s)?

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One viewpoint that may help with the intuition is that the Radon-Nikodym derivative is ... well, in most cases, it's a derivative. You know---derivative, like you first learned in kindergarten (or maybe freshman calculus). It's not just an analogy, it's a real genuine limit of a familiar sort.

Chapter Eight in our text Real Analysis (Bruckner$^2$*Thomson) develops these ideas if you care to look. You can download a PDF from here.