Optimal Transport: Stability and Counterexamples

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

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

Explores optimal transport in heat equations and metric spaces.

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

Explores implicit schemes in numerical analysis, emphasizing stability and convergence properties in solving differential equations.

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

Covers the joint equidistribution of CM points and the ergodic decomposition theorem in compact abelian groups.

Explores the implications of Baire Theorem in functional analysis and metric spaces.

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

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.