This paper contains a
definition and a construction of a Radon-Nikodym derivative of a a-additive set
function with respect to a measure on a σ-lattice, that is, a family of sets closed
under countable unions and countable intersections. This derivative is characterized
in terms of its indefinite integral, and it is shown how the conditional expectation of
an integrable random variable with respect to a σ-lattice, as defined by Brunk, can
be obtained as a Radon-Nikodym derivative of the set function determined by the
indefinite integral of the random variable.