The Brunn Minkowski inequality asserts that the Lebesgue measure is log-concave.
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The Brunn Minkowski inequality also leads to Anderson's theorem in statistics.
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For p \ geq1, the Minkowski distance is a metric as a result of the Minkowski inequality.
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For " p " < ", the Minkowski inequality and the monotone convergence theorem imply that
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His results in this field include Milman's reverse Brunn Minkowski inequality and the quotient of subspace theorem.
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In mathematical analysis, the "'Minkowski inequality "'establishes that the L " p " spaces are normed vector spaces.
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H�lder's inequality is used to prove the Minkowski inequality, which is the triangle inequality in the space, and also to establish that is the dual space of for.
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:Numerous geometric inequalities, such as the Brunn & ndash; Minkowski inequality for convex bodies and Minkowski's first inequality, are special cases of the Alexandrov & ndash; Fenchel inequality.
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The proof on the inequality follows directly from Brunn-Minkowski inequality between a set S and a ball with radius \ epsilon, i . e . B _ \ epsilon = \ epsilon B _ 1.
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Milman's theorem states that one can replace one of the bodies by its image under a properly chosen volume-preserving linear map so that the left-hand side of the Brunn & ndash; Minkowski inequality is bounded by a constant multiple of the right-hand side.
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