Optimal Transport: Disintegration Theorem

Related lectures (30)

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Explores mixing properties of infinite measure preserving systems, focusing on suspensions, Govers transformations, and Lorentz gas.

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Covers implicit schemes in numerical analysis for solving partial differential equations.

Explains setting up experiments with compactness, isometries, and quasi-isometry.

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

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

Discusses separation criteria and quotient spaces in topology, emphasizing their applications and theoretical foundations.

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

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Covers weak derivatives, their properties, and applications in functional analysis.

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

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

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Covers the Prokhorov Theorem in Optimal Transport, emphasizing support sets and optimality conditions.

Explains compact sets, convergence, and absolute convergence in real analysis.

Covers the concepts of sequences, convergence, and boundedness in mathematics.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

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