Nonstability of the inversion of the radon transform

Several examples of the distributions on the plane for which the distance in variation between their projections on an arbitrary one-dimensional direction is less than or equal to ε, but the uniform distance between their two-dimensional distribution functions is equal to 1/2, are constructed. Bibliography: 12 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 216, 1994, pp. 76–85. Translated by the author.