[Rado's Theorem](/theorems/6637) for Matroid Transversals is a result in [matroid theory](/page/Matroid%20Theory). It formalizes the assertion that let be a matroid on a finite set with rank function , and let . There exist distinct elements such that is independent in if and only if \begin{align } r N\left(\bigcup {i \in S} B i\right) \ge |S| \end{align } for every.