In mathematics, the Radon-Nikodym theorem is a result in functional analysis that states that if a measure is absolutely continuous with respect to another sigma-finite measure then there is a measurable function f, taking values in [0,∞], on the underlying space such that
The theorem is named for Johann Radon, who proved the theorem for the special case where the underlying space is in 1913, and for Otto Nikodym who proved the general case in 1930.