"A probabilistic error estimate of quadrature formulas accurate for
Haar polynomials" Kirillov K.A. 
Quadrature formulas possessing the Haar dproperty (i.e., the formulas that are accurate for Haar functions of groups with the numbers not exceeding a given number d) are studied. Previously it was proved that these quadrature formulas have the best order of convergence to zero for the error functional on the classes S_{p} consisting of the functions with the fast convergent FourierHaar series. In this paper we obtain a probabilistic error estimate on the classes S_{p} for the quadrature formulas possessing the Haar dproperty. According to this estimate, for a function randomly chosen from S_{p} the order of convergence to zero for the error functional is better with an arbitrarily high probability than that obtained previously. In 1970s, I.M. Sobol studied the quadrature formulas with nodes that form П_{τ} grids; these formulas are also accurate for the Haar functions. This paper generalizes the result obtained by Sobol to the case of arbitrary quadrature formulas possessing the Haar dproperty. Keywords: Haar dproperty, error of quadrature formula, S_{p} classes of functions.

