Optimal Transport: Analysis IV

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 2 of 4

Lebesgue Integral: Comparison with Riemann

Explores the comparison between Lebesgue and Riemann integrals, demonstrating their equivalence when the Riemann integral exists.

Multivariable Integral Calculus

Covers multivariable integral calculus, including rectangular cuboids, subdivisions, Douboux sums, Fubini's Theorem, and integration over bounded sets.

Sigma Field: Random Variables

Explores sigma fields generated by random variables and their connection to measurable functions.

Fundamental Theorem of Calculus: Integrability, Anti-derivatives, Integration by Parts

Covers integrability, anti-derivatives, and integration by parts in calculus.

Riemann Integral: Properties and Generalization

Explores characterizations and generalizations of the Riemann integral, showcasing its properties and applications.

Functional Calculus: Simple Functions

Covers the extension of functional calculus to simple functions and the concept of *-homomorphism.

Uneigentliche Integrale: Singularities and Infinite Integration Intervals

Covers improper integrals with singularities and infinite intervals.

Fubini Theorem on Closed Rectangles

Explores the Fubini theorem on closed rectangles in R², discussing integrability, iterated integrals, and compact sets.

Integration: Taylor Approximation & Convex Functions

Covers Taylor approximation, convex functions, and integrable properties.

Analysis IV: Measurable Sets and Properties

Covers the concept of outer measure and properties of measurable sets.