Exercise 1.1.17 (Bolyai-Gerwien problem)

Let $P, Q$ be polytopes in $ℝ^{d}$ . Suppose that $P$ can be partitioned into finitely many sub-polytopes $P_{1}, \dots, P_{n}$ which, after being rotated and translated, form new polytopes $Q_{1}, \dots, Q_{n}$ which are an almost disjoint cover of $Q$ . Conclude that $P$ and $Q$ have the same Jordan measure.

Exercise 1.1.17 (Bolyai-Gerwien problem)

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