Gel’fand widths of Sobolev classes of functionsin the average setting

In this article, we study univariate Sobolev spaces and multivariate Sobolev spaces with mixed derivatives equipped with the Gaussian measures in the average and probabilistic settings. New sharp asymptotic orders of the Gel’fand N -widths of the corresponding Sobolev classes in the Lebesgue spaces are obtained in these settings.