  Using multiplicative ergodic theory we prove two formulae describing the
relationships between different joint spectral radii for sets of bounded linear
operators acting on a Banach space. In particular we recover a formula
previously proved by V. S. Shulman and Yu. V. Turovski\u{\i} using
operator-theoretic ideas. As a byproduct of our method we answer a question of
J. E. Cohen on the limiting behaviour of the spectral radius of a measurable
matrix cocycle.
