Lectures related to Carathéodory's criterion

Covers the concept of integer cones and Carathéodory's theorem with illustrative examples.

Covers measurability, independence of sets, sigma-algebras, cylinder sets, co-algebras, uniqueness, and extension of measures.

Carathéodory's Theorem and Dimension Bound

Explores Carathéodory's Theorem and its dimension implications for set representation.

Probability Measures and Random Variables

Covers the Caratheodory extension theorem, uniqueness and existence of probability measures, Bernoulli random variables, and spaces of random variables.