  In this paper, we first define the concept of the limit average range of a
function defined on $[0,1]$ and taking values in a Hausdorff locally convex
topological vector space (locally convex space) $X$. Then, we present
characterizations of the primitive $F:[0,1] \to X$ of an integrable by
seminorms function $f:[0,1] \to X$ in terms of the limit average range of $F$.
It is shown that the limit average range characterizes the integral by
seminorms better then the usual differential.
