The title is borrowed from the seminal paper by Furstenberg from 1963.
In the introduction of that paper he raises the question whether there is a limit law, similar to the law of large numbers, for products $$ X_{1}X_{2}X_{3}...X_{n} $$ as $n\rightarrow\infty$, where $X_{i}$ are transformations chosen at random. Such products appear in several contexts within mathematics as well as in other sciences. The transformations could be bounded linear operators, holomorphic maps or just elements in an abstract group. I will discuss one answer to this general question using metric spaces, their functionals, and sub additive ergodic theory. Based on joint work with S. Gouëzel.