A translation $T_w$ is the action of translating an entire function by $w$, i.e., $(T_wf)(z)=f(z+w)$. In 1996 Weiss constructed an abundance of translation invariant probability measures on the space of entire functions.

In this talk we will extend this exact result to holomorphic functions of $\mathbb C^d$, for any $d\ge 1$ answering a question posed by T-C Dinh and N. Sibony in 2018. This talk is based on a joint work with B. Weiss.