  In this paper we develop a notion of measure theory over boolean toposes
which is analogous to noncommutative measure theory, i.e. to the theory of von
Neumann algebras. This is part of a larger project to study relations between
topos theory and noncommutative geometry. The main result is a topos theoretic
version of the modular time evolution of von Neumann algebra which take the
form of a canonical R+*-principal bundle over any integrable locally separated
boolean topos.
