A concise proof of the Radon-Nikodym theorem is given using nonstandard analysis.
Ma, S Li, and Y Shi, Radon-Nikodym theorem in signed Loeb space, Wuhan University Journal of Natural Sciences,15(2010), 21-24
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A Short Nonstandard Proof of the Radon-Nikodym Theorem
A concise proof of the Radon-Nikodym theorem is given using nonstandard analysis.