Optimal Transport: Disintegration Theorem

Related lectures (30)

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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.

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

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.

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

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