2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66271Suppose that $S$ is an incomplete inner product space. A. Dvurečenskij shows that there are no finitely additive states on orthogonally closed subspaces, $F(S)$, of $S$ that are regular with respect to finitely dimensional spaces. In this note we show that the most important special case of the former result--the case of the evaluations given by vectors in the ``Gleason manner''--allows for a relatively simple proof. This result further reinforces the conjecture that there are no finitely additive states on $F(S)$ at all.Rings and Algebrastext