On Convergence and Compactness in Variation with a Shift of Discrete Probability Laws

We consider a class of discrete distribution functions whose characteristic are separated from zero, i.e., their absolute values larger than certain positive constant on the entire real line. This is rather wide: it contains infinitely divisible functions, lattice distributions have no zeroes line, and also with jump greater 1/2. Recently, we demonstrated in our study that corresponding to elements this admit Lévy–Khinchin type representation nonmonotonic spectral function. Thus, included set quasi-infinitely functions. Using these representations, obtained limit theorems compactness convergence variation for sequences class. paper devoted analogous results concerning compactness, but somewhat weakened variation. Changing notably expands applicability results.