  As it is known, Gleason's theorem is not applicable for a two-dimensional
Hilbert space since in this situation Gleason's axioms are not strong enough to
imply Born's rule thus leaving room for a dispersion-free probability measure
i.e., one that has only values 0 and 1. To strengthen Gleason's axioms one must
add at least one more assumption. But, as it is argued in the present paper,
alternatively one can give up the lattice condition lying in the foundation of
Gleason's theorem. Particularly, the lattice structure based on the closed
linear subspaces in the Hilbert space could be weakened by the requirement for
the meet operation to exist only for the subspaces belonging to commutable
projection operators. The paper demonstrates that this weakening can resolve
the problem of the dispersion-free probability measure in the case of a qubit.
