Sard's theorem for hyper-Gevrey functionals on the Wiener space (Q1891823)

Sard's theorem has been shown to be non valid on the Wiener space if one only assumes that the functional is smooth in Malliavin's sense. In this work, one constructs classes of functionals, called hyper-Gevrey functionals, and one proves that the image by such a functional \(g\) of the restriction of Wiener's measure to singular points of \(g\) has zero Hausdorff dimension. In the appendix, one checks that this theorem can be applied to the solution of stochastic differential equations with Gevrey class coefficients.