  The paper presents a general duality theory for vector measure spaces taking
its origin in the author's papers written in the 1960s. The main result
establishes a direct correspondence between the geometry of a measure in a
vector space and the properties of the space of measurable linear functionals
on this space regarded as closed subspaces of an abstract space of measurable
functions. An example of useful new features of this theory is the notion of a
free measure and its applications.
