Probability distribution for Omega in open-universe inflation

The problem of making predictions in an eternally inflating universe that thermalizes by bubble nucleation is considered. A recently introduced regularization procedure is applied to find the probability distribution for the ensemble of thermalized bubbles. The resulting probabilities are shown to be independent of the choice of the time parametrization. This formalism is applied to models of open ''hybrid'' inflation with Omega<1. Depending on the parameters of the model, the probability distribution for Omega is found to have a peak either very close to Omega=1, or at an intermediate value of Omega in the range O.03 less than or equal to Omega<1.