  We show that properties of pairs of finite, positive and regular Borel
measures on the complex unit circle such as domination, absolute continuity and
singularity can be completely described in terms of containment and
intersection of their reproducing kernel Hilbert spaces of `Cauchy transforms'
in the complex unit disk. This leads to a new construction of the classical
Lebesgue decomposition and proof of the Radon--Nikodym theorem using
reproducing kernel theory and functional analysis.
