  We study the problem of the integral geometry, in which the functions are
integrated over hyperplanes in the $n$-dimensional Euclidean space, $n=2m+1$.
The integrand is the product of a function of $n$ variables called the density
and weight function depending on $2n$ variables. Such an integration is called
here the weighted Radon transform, which coincides with the classical one if
the weight function is equal to one. It is proved the uniqueness for the
problem of determination of the surface on which the integrand is
discontinuous.
