Lectures related to Lévy's continuity theorem

Properties of Complete Spaces

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

Monotone Convergence: Fatou's Lemma

Explores monotone convergence, dominated convergence, and Fatou's lemma with practical examples.

Pointwise Convergence of Fourier Series

Explores the pointwise convergence of Fourier series and its applications in optimal transport.

Martingales and Brownian Motion

Discusses convergence, martingales, Brownian motion, joint laws, testing procedures, and stop times.

Convergence Theorems

Explores convergence theorems and the unique radius for series convergence.