A counterexample to the strong Skorokhod representation theorem

Abstract Recently, a strengthened version of the Skorokhod representation theorem, introduced in Brzeźniak et al. (Potential Anal 49:131–201, 2018), has been applied in proofs of existence of martingale solutions to various stochastic PDEs in more than two dozens papers. In this note we show that, unfortunately, the Skorokhod-type theorem from Brzeźniak et al. (Potential Anal 49:131–201, 2018) is wrong and cannot be corrected.