Blaschke 1916: every uniformly-bounded sequence of convex bodies in ℝ^d has a Hausdorff-convergent subsequence. Compactness of convex-bodies-with-Hausdorff-metric. Used in isoperimetric-type inequalities, geometric tomography.
Blaschke 1916: every uniformly-bounded sequence of convex bodies in ℝ^d has a Hausdorff-convergent subsequence. Compactness of convex-bodies-with-Hausdorff-metric. Used in isoperimetric-type inequalities, geometric tomography.