Let \(D_0\) and \(D \supset \overline {D_0}\) be two concentric plane, open disks. It is well known that the restriction to \(D_0\) of a function u supported in D cannot be determined from the restriction of its Radon transform \(R u(L)\) to the set of lines L that intersect \(D_0\) . It has been conjectured that the same is true if \(D_0\) and \(D \supset \overline {D_0}\) are arbitrary open, bounded, convex subsets of the plane. A theorem related to this conjecture is presented.