A space of fuzzy sets $M$ is considered as a base of a
quantum structure model (fuzzy quantum logic, see \cite{5}).
A state is a morphism from $M$ to the unit interval, an
observable is a morphism from Borel sets to $M$. The
subspace $L^p$ of observables is studied and it is proved
that $L^p$ considered with the corresponding pseudometric is
a complete pseudometric space.
