Lotus BlogTheory - [T9]
Definitions
During the lectures we have seen how strictly related Measure Theory and Probability Theory are. In fact we can easily observe how Kolmogorov, used the axioms existing in the Measure Theory branch of Mathematics to formulate the axioms that formalize the definition of Probability Theory.
Relation between Measure Theory and Probability Theory
Measure Theory lays the foundations of Probability Theory, as it unifies the discrete and the continuous cases, and makes the difference a question of which measure is used. Furthermore, it covers distributions that are neither discrete nor continuous nor mixtures of the two. By utilizing the concepts and techniques from measure theory, probability theory can rigorously define and analyze probabilities, establish important properties, and develop advanced probabilistic models