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Brunn-Minkowski Inequality

The $n$th root of the Content of the set sum of two sets in Euclidean $n$-space is greater than or equal to the sum of the $n$th roots of the Contents of the individual sets.

See also Tomography


Cover, T. M. ``The Entropy Power Inequality and the Brunn-Minkowski Inequality'' §5.10 in Open Problems in Communications and Computation. (Ed. T. M. Cover and B. Gopinath). New York: Springer-Verlag, p. 172, 1987.

Schneider, R. Convex Bodies: The Brunn-Minkowski Theory. Cambridge, England: Cambridge University Press, 1993.

© 1996-9 Eric W. Weisstein