The Radon-Nikodým theorem for vector measures and integral representation of operators on Banach function spaces

A well known vector measure version of the Radon-Nikodým theorem—comparing two vector measures— can also be interpreted in terms of factorization of an operator—the one associated to the first measure— through the one associated to the second one. Using several results published in recent years, we show the factorization version of this Radon-Nikodým theorem and its applications in the setting of the Operator Theory and the Harmonic Analysis.