The aim of this note is to reduce a number of assumptions in the recent paper of W. Bryc by showing that some of them imply the others and to give alternative, simpler proofs of some of Bryc's results.
"A few remarks on Bryc's paper on random fields with linear regressions." Ann. Probab. 30 (3) 1486 - 1491, July 2002. https://doi.org/10.1214/aop/1029867134