Uniqueness and nonuniqueness of solution of the totality of the first kind equations equivalent with respect to a given accuracy

A linear equation of the first kind with a perturbed operator is considered. It is assumed that a level of perturbation is known. The totality of equations equivalent with respect to a given accuracy is introduced. For such a totality, new definitions of uniqueness and nonuniqueness are formulated. Algorithms for investigation of the (non)uniqueness are constructed. Examples of applications are given in the X-ray structural analysis and the diffraction method.