Radon-Nikodym Derivative

When a measure lambda is absolutely continuous with respect to a positive measure mu, then it can be written as


By analogy with the first fundamental theorem of calculus, the function f is called the Radon-Nikodym derivative of lambda with respect to mu. Sometimes it is denoted dlambda/dmu or Dlambda/Dmu.

See also

Absolutely Continuous, Complex Measure, Fundamental Theorems of Calculus, Lebesgue Measure, Polar Representation, Radon-Nikodym Theorem

This entry contributed by Todd Rowland

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Cite this as:

Rowland, Todd. "Radon-Nikodym Derivative." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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