Problem 1356 (difficulty: 6/10)

Prove that a bounded set \(\displaystyle K\subset\R^n\) is Jordan-measurable if and only if it cuts all bounded open sets ``properly'' i.e. for all bounded open set \(\displaystyle X\subset\R^n\) one has \(\displaystyle b(X\cap K)+b(X\setminus K)=b(X)\).

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