We show, by a simple counterexample, that the main result in a recent paper by H. Van Zanten [Electronic Communications in Probability 7 (2002), 215-222] is false. We eventually point out the origin of the error.
"Weak Convergence to Ocone Martingales: a Remark." Electron. Commun. Probab. 9 172 - 174, 2004. https://doi.org/10.1214/ECP.v9-1121