In 1733, Demover-Laplace proved by reasoning and concluded that the limit distribution of the binomial distribution was a normal distribution. Later, he made improvements on the original basis and proved that more than the binomial distribution satisfies This condition, any other distribution is possible, and has made a great contribution to the development of the central limit theorem. After that, the development of the law of large numbers has stalled. Until the 20th century, Lyapunov made his own innovation on the basis of Laplace's theorem. He came up with the characteristic function method and extended the study of the law of large numbers to the function level, which has a great influence on the development of the central limit theorem. Significance. By 1920, mathematicians began to explore the conditions under which the central limit theorem was generally established. Only then did the Lindbergh condition and the Fehler condition published later, these results contributed to the development of the central limit theorem.
After hundreds of years of development, the system of the laws of large numbers has been perfected, and more and more extensive laws of large numbers have emerged, such as Chebyshev’s law of large numbers, Sinchin’s law of large numbers, Poisson’s law of large numbers, and Marko The law of large numbers and so on. It is the constant research of these mathematicians that the law of large numbers can be developed so quickly and be perfected.