Limites approximatives sur l'espace de Wiener

We use a stochastic integral which was first constructed by Nualart, Zakai and Ogawa, to show, for the variables of the second Wiener chaos, that the existence of this integral imply that these variables possess an approximate limit with respect to measurable norms defined by Gross. Moreover, this limit does not depend on the choice of the norm. Furthermore, we show that measurable norms possess an approximate limit with respect to quadratic norms. The main argument is a correlation inequality proved by Hargé.