:Any two bounded subsets (of 3-space) with non-empty interior, are equi-decomposable by translations and rotations. This can be illustrated by saying that a marble can be cut up into finitely many pieces and reassembled into a planet. Note that in the decomposition, the pieces are not measurable, and so they will not have "reasonable" boundries. |
:Any two bounded subsets (of 3-space) with non-empty interior, are equi-decomposable by translations and rotations. This can be illustrated by saying that a marble can be cut up into finitely many pieces and reassembled into a planet. Note that in the decomposition, the pieces are not measurable, and so they will not have "reasonable" boundaries. |