Advanced analysis II

Related lectures (32)

Page 2 of 4

Explores the construction of measures, emphasizing positive functionals and their connection to the Riesz-Kakutani Theorem.

Covers extreme values of continuous functions on compact sets and differentiability.

Covers the Cantor-Heine theorem, discussing uniform continuity and compactness.

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

Introduces the course on measure and integration, focusing on developing a new theory to overcome the limitations of the Riemann integral.

Covers the properties of the Lebesgue measure and its existence.

Explores the construction of the Lebesgue function on the Cantor set and its unique properties.

Explores continuous functions on compact sets, discussing boundedness and extremum values.

Explores the Stone-Weierstrass theorem, proving uniform density of specific function families on compact sets.

Delves into advanced analysis topics, emphasizing continuity, limits, and uniform continuity.