MEASURE ON A SUBSPACE OF FRW SOLUTIONS AND THE FLATNESS PROBLEM OF STANDARD COSMOLOGY

We use the metric on the space of gravity fields given by DeWitt to co nstruct a unique kinematic measure on the space of FRW simple fluids a nd show that when the mass parameter Omega is used as a coordinate thi s measure is singular at Omega = 1. This singularity, combined with th e time evolution of Omega, distorts distributions of Omega values to b e concentrated in the neighborhood of 1 at early times. It is a distor ted distribution of Omega values that sometimes misleads the casual ob server to conclude that Omega must be exactly equal to 1.