  The Wigner function shares several properties with classical distribution
functions on phase space, but is not positive-definite. The integral of the
Wigner function over a given region of phase space can therefore lie outside
the interval [0,1]. The problem of finding best-possible upper and lower bounds
for a given region is the problem of finding the greatest and least eigenvalues
of an associated Hermitian operator. Exactly solvable examples are described,
and possible extensions are indicated.
