  This note deals with quasi-states on the two-dimensional torus. Quasi-states
are certain quasi-linear functionals (introduced by Aarnes) on the space of
continuous functions. Grubb constructed a quasi-state on the torus, which is
invariant under the group of area-preserving diffemorphisms, and which moreover
vanishes on functions having support in an open disk. Knudsen asserted the
uniqueness of such a quasi-state; for the sake of completeness, we provide a
proof. We calculate the value of Grubb's quasi-state on Morse functions with
distinct critical values via their Reeb graphs. The resulting formula coincides
with the one obtained by Py in his work on quasi-morphisms on the group of
area-preserving diffeomorphisms of the torus.
