Lectures related to Probability Theory: Integration and Convergence

Basic Properties of Conditional Expectation

Covers basic properties of conditional expectation and Jensen's inequality in probability theory.

Covers the basics of probability theory, including probability spaces, random variables, and measures.

Covers the properties of complete spaces, including completeness, expectations, embeddings, subsets, norms, Holder's inequality, and uniform integrability.

Generalization Error

Explores tail bounds, information bounds, and maximal leakage in the context of generalization error.

Approximation by Smooth Functions

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

Analysis IV: Convergence Theorems and Integrable Functions

Covers convergence theorems and integrable functions, including the Lebesgue integral and Borel-Cantelli sets.