  Integral foliated simplicial volume is a version of simplicial volume
combining the rigidity of integral coefficients with the flexibility of measure
spaces. In this article, using the language of measure equivalence of groups we
prove a proportionality principle for integral foliated simplicial volume for
aspherical manifolds and give refined upper bounds of integral foliated
simplicial volume in terms of stable integral simplicial volume. This allows us
to compute the integral foliated simplicial volume of hyperbolic 3-manifolds.
This is complemented by the calculation of the integral foliated simplicial
volume of Seifert 3-manifolds.
