are exponential distributions. "Memoryless" means that if is a random variable with such a distribution, then for any numbers , . Verification of conditions of characterization theorems in practice is possible only with some error , i.e., only to a certain degree of accuracy. Such a situation is observed, for instance, in the cases where a sample of finite size is considered. That is why there arises the following natural question. Suppose that the conditions of the characterization theorem are fulfilled not exactly but only approximately. May we assert that the conclusion of the theorem is also fulfilled approximately? The theorems in which the problems of this kind are considered are called stability characterizations of probability distributions. See also Characterization (mathematics) References Probability theorems Theorems in statistics