# Minkowski's First Inequality For Convex Bodies - Statement of The Inequality

Statement of The Inequality

Let K and L be two n-dimensional convex bodies in n-dimensional Euclidean space Rn. Define a quantity V1(K, L) by

where V denotes the n-dimensional Lebesgue measure and + denotes the Minkowski sum. Then

with equality if and only if K and L are homothetic, i.e. are equal up to translation and dilation.

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Loomis–Whitney Inequality - Statement of The Inequality
... consider the projections For each 1 ≤ j ≤ d, let Then the Loomis–Whitney inequality holds Equivalently, taking ...

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It is commonplace that a problem stated is well on its way to solution, for statement of the nature of a problem signifies that the underlying quality is being transformed into determinate distinctions of terms and relations or has become an object of articulate thought.
John Dewey (1859–1952)

It is commonplace that a problem stated is well on its way to solution, for statement of the nature of a problem signifies that the underlying quality is being transformed into determinate distinctions of terms and relations or has become an object of articulate thought.
John Dewey (1859–1952)

Nature is unfair? So much the better, inequality is the only bearable thing, the monotony of equality can only lead us to boredom.
Francis Picabia (1878–1953)

The new statement will comprise the skepticisms, as well as the faiths of society, and out of unbeliefs a creed shall be formed. For, skepticisms are not gratuitous or lawless, but are limitations of the affirmative statement, and the new philosophy must take them in, and make affirmations outside of them, just as much as must include the oldest beliefs.
Ralph Waldo Emerson (1803–1882)