Definition:Equidecomposable

Two sets $$S, T \subset \mathbb{R}^n \ $$ are said to be equidecomposable if there exists a set

$$X = \left\{{A_1, \dots, A_m }\right\} \subset \mathcal{P} \left({\mathbb{R}^n}\right) $$,

the latter being the power set of $$\mathbb{R}^n \ $$, such that both $$S \ $$ and $$T \ $$ are decomposable into the elements of $$X \ $$.