Distances between measures from 1-dimensional projections as implied by continuity of the inverse radon transform

Summary Distances between measures on IR ^d are determined from distances between their 1-dimensional projections. The method employed involves considering the 1-dimensional projections to be the Radon transform of the measures. Crucial to the main theorem is a continuity result for the inverse Radon transform. Focus is restricted to the Prohorov, dual bounded Lipschitz and d _k metrics which metrize weak convergence of probability measures. These metrics are related to each other and to the Sobolev norms. The d _k results extend from measures to generalized functions.Partially supported by NSF Grant No. MCS-81-01895Partially supported by NSF Grant No. MCS-82-01627 and support from the Mellon Foundation