Optimal Transport: Analysis IV

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Related lectures (32)

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Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Differential Forms Integration

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

Iterated Integrals: Order, Properties, and Applications

Explores iterated integrals, their order, properties, and applications in practical scenarios.

Integration by Parts

Covers integration by parts, including practical applications and mnemonic aids.

Integration Techniques: Change of Variable and Integration by Parts

Explores advanced integration techniques such as change of variable and integration by parts to simplify complex integrals and solve challenging integration problems.

Probability Theory: Integration and Convergence

Covers topics in probability theory, focusing on uniform integrability and convergence theorems.

Harmonic Forms: Main Theorem

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

Lebesgue Integral: Definition and Properties

Explores the Lebesgue integral, where functions self-select partitions, leading to measurable sets and non-measurable complexities.

Fubini's Theorem: Multiple Integrals

Explores Fubini's Theorem for multiple integrals, emphasizing the n=2 case.

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