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A short solution to the Busemann-Petty problem

Abstract : A unified analytic solution to the Busemann-Petty problem was recently found by Gardner, Koldobsky and Schlumprecht. We give an elementary proof of their formulas for the inverse Radon transform of the radial function rho(K) of an origin-symmetric star body K.
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Franck Barthe, Matthieu Fradelizi, Bernard Maurey. A short solution to the Busemann-Petty problem. Positivity, Springer Verlag, 1999, 3 (1), pp.95--100. ⟨10.1023/A:1009777119957⟩. ⟨hal-00693894⟩

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