Last Updated
：2025/11/30
Hadwiger's theorem
Proper noun
Japanese Meaning
Hadwigerの定理は、ユークリッド空間Rⁿにおける凸体に定義される評価関数（連続かつ剛体運動に対して不変なもの）が、固有体積（または同値なクォルマス積分）の線形結合として一意に表されるという、幾何学における基本的な定理です。
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(geometry) A theorem asserting that every valuation on convex bodies in Rⁿ that is continuous and invariant under rigid motions of Rⁿ is a linear combination of the quermassintegrals (or, equivalently, of the intrinsic volumes).
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Hadwiger's theorem
In his lecture, the professor used Hadwiger's theorem to show that any continuous valuation on convex bodies in Rn that is invariant under rigid motions can be expressed as a linear combination of intrinsic volumes.
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In his lecture, the professor used Hadwiger's theorem to show that any continuous valuation on convex bodies in Rn that is invariant under rigid motions can be expressed as a linear combination of intrinsic volumes.
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