In this paper we prove that for a finite-dimensional real normed space V, every bounded mean zero function f∈L∞([0,1];V) can be written in the form
f=g∘T−g for some g∈L∞([0,1];V) and some ergodic invertible measure preserving transformation T of [0,1].
Our method moreover allows us to choose g, for any given ε>0, to be such that ∥g∥∞≤(SV+ε)∥f∥∞, where SV is the Steinitz constant corresponding to V