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Coverings by Convex Bodies and Inscribed Balls by Kadets, Vladimir is a scholarly article available to read on EtoBox.

What is Coverings by Convex Bodies and Inscribed Balls about?

Let $H$ be a Hilbert space. For a closed convex body $A$ denote by $r(A)$ the supremum of radiuses of balls, contained in $A$. We prove, that $\sum_{n=1}^\infty r(A_n) \ge r(A)$ for every covering of a convex closed body $A \subset H$ by a sequence of convex closed bodies $A_n$, $n \in \N$. It looks like this fact is new even for triangles in a 2-dimensional space.

Author

Kadets, Vladimir

Published

2003

Language

EN