Abstract
We recall Bourgain's conjecture on the upper bound for the main moments of inertia of a multidimensional body in the isotropic state. We also recall the currently known bounds obtained by Bourgain and Klartag. Then we evaluate the moments of inertia of the multidimensional ball and of the multidimensional cube, and state a conclusive comment corroborating the Bourgain's conjecture.
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