Multiplicative constants and maximal measurable cocycles in bounded cohomology

Multiplicative constants are a fundamental tool in the study of maximal representations. In this paper we show how to extend such notion, and the associated framework, to measurable cocycles theory. As an application of this approach, we define and study the Cartan invariant for measurable $textup{PU}(m,1)$-cocycles of complex hyperbolic lattices.