  We present a framework, compliant with the general canonical principle of
statistical mechanics, to define measures on the set of pure Gaussian states of
continuous variable systems. Within such a framework, we define two specific
measures, referred to as `micro-canonical' and `canonical', and apply them to
study systematically the statistical properties of the bipartite entanglement
of n-mode pure Gaussian states (as quantified by the entropy of a subsystem).
We rigorously prove the "concentration of measure" around a finite average,
occurring for the entanglement in the thermodynamical limit in both the
canonical and the micro-canonical approach. For finite n, we determine
analytically the average and standard deviation of the entanglement (as
quantified by the reduced purity) between one mode and all the other modes.
Furthermore, we numerically investigate more general situations, clearly
showing that the onset of the concentration of measure already occurs at
relatively small n.
