Abstract
We study measures on \(\mathbb{R}^n\) which are product measures for the usual Cartesian product structure of \(\mathbb{R}^n\) as well as for the polar decomposition of \(\mathbb{R}^n\) induced by a convex body. For finite atomic measures and for absolutely continuous measures with density \(d\mu/dx = e^{-V(x)}\), where V is locally integrable, a complete characterization is presented.
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F. Barthe: Partially supported by EPSRC grant 64 GR/R37210.
M. Csörnyei: Supported by the Hungarian National Foundation for Scientific Research, grant # F029768.
A. Naor: Supported in part by the Binational Science Foundation Israel-USA, the Clore Foundation and the EU grant HPMT-CT-2000-00037. This work is part of a Ph.D. thesis being prepared under the supervision of Professor Joram Lindenstrauss.
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© 2003 Springer-Verlag Berlin/Heidelberg
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Barthe, F., Csörnyei, M., Naor, A. (2003). A Note on Simultaneous Polar and Cartesian Decomposition. In: Milman, V.D., Schechtman, G. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1807. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36428-3_1
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DOI: https://doi.org/10.1007/978-3-540-36428-3_1
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