Peculiarities of the large numbers law in conditions of disturbances of statistical stability

Abstract

Peculiarity of the low of large numbers in conditions of disturbance of statistical stability is researched. It is found that for random sequences sample average may converges to definite number, tends to plus or minus infinity, or fluctuates in definite interval. Number theorems describe the low of large numbers for hyper–random sequences are proved. It is found that sample average of hyper–random variable may converges to definite number, to a set of definite numbers, fluctuates in non–intersecting intervals of conditional boundaries, fluctuates in a interval of unconditional boundaries, or tends to plus or minus infinity. Differences in convergent variants of random and hyper–random sequences must be taken into account when researches of radio devices and systems are led.