Conclusion: The Central Limit Theorem as a Link Between Classical and Modern Probability Theory

Abstract

During the period between the two world wars, modern probability theory emerged as a mathematical subdiscipline—with the typical formation of concepts, main theorems and methods—by integrating the subfields of axiomatics (including aspects of measure theory), strong laws of large numbers, stochastic processes, and limit theorems for distributions of sums of random variables, which at first were related by little more than the shared generic term “probability.” Only this last field of limit theorems could point to any significant contributions in the 18th and particularly the 19th centuries, and it played an especially important role during the transition from classical to modern probability theory. In the following summary of the most important aspects of this book, that role will be examined more closely. In so doing, it is particularly important to pursue the question of how the CLT can be understood as “classical” content of probability theory and what types of changes it underwent while crossing over to modern probability.