Multivariate probabilistic approximation in wavelet structure

Let $$\varphi _0 (x,y): = \{ _{0,}^{1,} {\text{ }}_{otherwise}^{{\text{x,y}} \geqslant {\text{0}}} $$ and F(x,y) be a continuous distribution function on R². Then there exist linear wavelet operators L_n(F,x,y) which are also distribution function and where the defining them mother wavelet is φ₀(x,y). These approximate F(x,y) in the supnorm. The degree of this approximation is estimated by establishing a Jackson type inequality. Furthermore we give generalizations for the case of a mother wavelet φ₀, which is just any distribution function on R² also we extend these results in R²,r>2