Functional Analysis: Baire's Theorem

Related lectures (31)

Page 2 of 4

Explores examples and applications of the Cauchy-Lipschitz theorem in sequences and Banach spaces.

Introduces linear and bounded operators, compact operators, and the Banach space.

Covers stability in optimal transport and provides examples of discontinuous optimal solutions.

Explores optimal transport in heat equations and metric spaces.

Explores limits, convergence, and boundedness of functions and sequences.

Covers the convergence of Cauchy sequences and its applications in theorems.

Explores the Banach Fixed Point Theorem, showing the uniqueness of fixed points in contraction mappings.

Covers Borel-Cantelli lemmas, laws of random variables, and convergence in probability.

Explores norms, distances, scalar products, and norm convergence in metric spaces.

Explores the Banach-Steinhaus theorem and the Closed Graph Theorem.