👉 At its core, the mathematical foundation of probability theory relies on measure theory and set theory. Probability is defined as a measure on a sample space, assigning non-negative real numbers to events in such a way that the probability of the entire sample space is 1 and the probability of the empty set is zero. This measure must satisfy countable additivity, meaning the probability of a union of disjoint events equals the sum of their individual probabilities. This rigorous framework ensures consistency and allows for advanced concepts like conditional probability, independence, and stochastic processes to be mathematically precise and applicable across various fields.
