  We study the computational content of the Radon-Nokodym theorem from measure
theory in the framework of the representation approach to computable analysis.
We define computable measurable spaces and canonical representations of the
measures and the integrable functions on such spaces. For functions f,g on
represented sets, f is W-reducible to g if f can be computed by applying the
function g at most once. Let RN be the Radon-Nikodym operator on the space
under consideration and let EC be the non-computable operator mapping every
enumeration of a set of natural numbers to its characteristic function. We
prove that for every computable measurable space, RN is W-reducible to EC, and
we construct a computable measurable space for which EC is W-reducible to RN.
