Kolmogorov's Foundations

Kolmogorov's Foundations provide a rigorous mathematical framework for probability, defining it as a consistent set of rules that assign sizes or measures to possible events. He established axioms ensuring probabilities are well-defined, non-negative, and sum to one for all possible outcomes. This foundation allows us to model uncertainty precisely and develop advanced statistical methods, ensuring that probability theory is logically consistent and applicable across various fields, from science to finance. Essentially, Kolmogorov's work formalized the logical structure behind our intuitive understanding of chance and randomness.