如果 L 是在 R 谁的 n 中央( n-i )片有一样( n-i )维的措施 n-i (与适当密度)作为中央( n-i )起源对称的星身体 K 切,然后 K 和 L 的相应n维的措施 n 满足 n (K) n (L)。这为措施为体积扩大一条概括恐怖节定理到那。
If L is a star body in Rn whose central(n-i)-slices have the same(n-i)-dimensional measure μn-1(with appropriate density) as the central(n-i)-slices of an origin-symmetric star body K, then the corresponding n-dimensional measures μn of K and L satisfy μn(K)≤μn(L). This extends a generalized Funk's section theorem for volumes to that for measures.