We will formulate a type of Gauss' divergence formula on sets of functions which are greater than a specific value of which boundaries are not regular. Such formula was first established by L. Zambotti in 2002 with a profound study of stochastic processes. In this paper we will give a much shorter and simpler proof for his formula in a framework of the Malliavin calculus and give alternate expressions. Our approach also enables to show that such formulae hold in other Gaussian spaces.
"A type of Gauss' divergence formula on Wiener spaces." Electron. Commun. Probab. 14 457 - 463, 2009. https://doi.org/10.1214/ECP.v14-1498