Pettis in  obtained improved versions of some theorems of Mc-Shane . Pettis exploited the properties of meager or first category sets throughout his paper. As second category sets in a topological space of second category form a grill, an alternative approach to the results of Pettis via grills may well be conjectured. Indeed, such a grill and even arbitrary grills satisfying requisite conditions are employed in this article to achieve certain extended forms of some results of Pettis. © 2010 Springer-Verlag Italia.