Metric Spaces and Isometric Embeddings

Related lectures (30)

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Explores optimal transport in heat equations and metric spaces.

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Explores probability convergence, discussing conditions for random variable sequences to converge and the uniqueness of convergence.

Covers Lipschitz maps, compact domains, changing variables, counting problems, and probability of ideals.

Introduces metric spaces, topology, and continuity, emphasizing the importance of open sets and the Hausdorff property.

Explores the intrinsic geometry of regular surfaces and isometric transformations, including spheres and cylinders.

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

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Covers convergence, completeness, and properties of metric spaces and Banach spaces.

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