On the value of distributions at a point and the multiplicative products

The theory of multiplication between distributions has been developed by several authors (cf. the references in [5]). Recently M. Itano [5] defined the multiplication satisfying certain reasonable requirements. Such a multiplication was called normal by him. In his theory the notion of a value of a distribution at a point in the sense of S. Lojasiewicz [7] plays an important role. On the other hand, in our previous paper [11] the multiplication was defined by using the 5-sequences. The aim of the present paper is to unify these two approaches of defining multiplication. To this end we shall introduce the notion of a ^-sequence in a restricted sense in order to make clear the relationships among different approaches to the theory of multiplication between distributions. Let T be a distribution defined on R. If lim < Γ, pn> exists for every W->oo