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Distances between measures from 1-dimensional projections as implied by continuity of the inverse Radon transform. (English) Zbl 0555.28005
Distances between measures on \({\mathbb{R}}^ d\) 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.

28A33 Spaces of measures, convergence of measures
46E27 Spaces of measures
44A05 General integral transforms
60F05 Central limit and other weak theorems
62E20 Asymptotic distribution theory in statistics
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