We solve a problem posed by J. P. Burgess and R. D. Mauldin, and thus show that a result of theirs on conditional distributions and orthogonal measures cannot be improved.
R. J. Gardner. "A Note on Conditional Distributions and Orthogonal Measures." Ann. Probab. 10 (3) 877 - 878, August, 1982. https://doi.org/10.1214/aop/1176993802