  This paper is about the structure of all entrance laws (in the sense of
Dynkin) for time-inhomogeneous Ornstein-Uhlenbeck processes with L\'evy noise
in Hilbert state spaces. We identify the extremal entrance laws with finite
weak first moments through an explicit formula for their Fourier transforms,
generalising corresponding results by Dynkin for Wiener noise and nuclear state
spaces. We then prove that an arbitrary entrance law with finite weak first
moments can be uniquely represented as an integral over extremals. It is proved
that this can be derived from Dynkin's seminal work "Sufficient statistics and
extreme points" in Ann. Probab. 1978, which contains a purely measure theoretic
generalization of the classical analytic Krein-Milman and Choquet Theorems. As
an application, we obtain an easy uniqueness proof for T - periodic entrance
laws in the general periodic case. A number of further applications to concrete
cases are presented.
