Distances between measures from 1-dimensional projections as implied by continuity of the inverse radon transform |
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Authors: | Marjorie G Hahn Eric Todd Quinto |
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Institution: | (1) Department of Mathematics, Tufts University, 02155 Medford, MA, USA |
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Abstract: | 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 |
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