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The problem of bounding of the distance between the two bodies of volume$\varepsilon$ located inside the $n$-dimensional body $B$ of unit volume where$n \to \infty$ is considered. In some cases such distances are bounded byfunction depends on $\varepsilon$ but not depends on $n$. We consider caseswhen $B$ is a sphere or a cube.

The boundness of distance between two sets of fixed volume inside the multidimensional ball or cube