  We study a generalization of the Wigner function to arbitrary tuples of
hermitian operators. We show that for any collection of hermitian operators
A1...An , and any quantum state there is a unique joint distribution on R^n,
with the property that the marginals of all linear combinations of the
operators coincide with their quantum counterpart. In other words, we consider
the inverse Radon transform of the exact quantum probability distributions of
all linear combinations. We call it the Wigner distribution, because for
position and momentum this property defines the standard Wigner function. We
discuss the application to finite dimensional systems, establish many basic
properties and illustrate these by examples. The properties include the
support, the location of singularities, positivity, the behavior under symmetry
groups, and informational completeness.
