The first aim of this paper is to wonder to what extent we can generalize the central limit theorem of Gordin  under the so-called -projective criteria to ergodic stationary random fields when completely commuting filtrations are considered. Surprisingly it appears that this result cannot be extended to its full generality and that an additional condition is needed.
The authors are grateful to the referee for his useful remarks.
"On the central limit theorem for stationary random fields under -projective condition." Electron. Commun. Probab. 27 1 - 12, 2022. https://doi.org/10.1214/22-ECP486