Kernel density estimators for random fields satisfying an interlaced mixing condition

► A “Lindeberg CLT” for strictly stationary random fields is provided. ► These random fields are uniformly ρ′-mixing and satisfy a Lindeberg condition. ► This result is used to prove a CLT for some kernel estimators of probability density. ► The strictly stationary random fields are ρ′-mixing satisfying extra properties. ► Their random variables have continuous probability density and joint densities.