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A note on simultaneous polar and Cartesian decomposition

Abstract : We study measures on R(n) which are product measures for the usual Cartesian product structure of R(n) as well as for the polar decomposition of R(n) induced by a convex body. For finite atomic measures and for absolutely continuous measures with density dmu/dx = e(-V(x)) where V is locally integrable, a complete characterization is presented.
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  • HAL Id : hal-00693596, version 1


Franck Barthe, M Csornyei, A Naor. A note on simultaneous polar and Cartesian decomposition. GEOMETRIC ASPECTS OF FUNCTIONAL ANALYSIS, 2003, 1807 (?), pp.1--19. ⟨hal-00693596⟩



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