  We introduce the notion of pullback along a measurable cocycle and we use it
to extend the Borel invariant studied by Bucher, Burger and Iozzi to the world
of measurable cocycles. The Borel invariant is constant along cohomology
classes and has bounded absolute value. This allows to define maximal cocycles.
We conclude by proving that maximal cocycles are actually trivializable to the
restriction of the irreducible representation.
