Eternally inflating universes can contain large thermalized regions with different values of the constants of Nature and with different density fluctuation spectra. To find the probability for a `typical' observer to detect a certain set of constants, or a certain fluctuation spectrum, one needs to compare the volumes occupied by different types of regions. If the volumes are taken on an equal-time hypersurface, the results of such a comparison are extremely sensitive to the choice of the time variable t. Here, I propose a method of comparing the volumes which is rather insensitive to the choice of t. The method is then applied to evaluate the relative probability of different minima of the inflaton potential and the probability distribution for the density fluctuation spectra.

25 pages, 4 figures can be faxed on request