The stability problem is the question of to what extent the conclusion of a theorem is sensitive to small changes in the assumptions. Such description is, of course, vague until the questions of how to quantify the departures both from the conclusion and from the assumption are answered. The latter is to some extent arbitrary; in the characterization context, typically, stability reasoning depends on the ability to prove that small changes (measured with respect to some measure of smallness) in assumptions of a given characterization theorem result in small departures (measured with respect to one of the distances of distributions) from the normal distribution.