Lectures related to Vitali set

Probability Theory: Lecture 2

Explores toy models, sigma-algebras, T-valued random variables, measures, and independence in probability theory.

Minkowski's Theorems: Lattices and Volumes

Explores Minkowski's theorems on lattices, volumes, and set comparisons.

Lebesgue Integration: Cantor Set

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

Lattice Theory: Minkowski's Theorems

Delves into lattice theory, emphasizing Minkowski's theorems and their implications on lattice structures.

The Riesz-Kakutani Theorem

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

Lebesgue Measure: Properties and Existence

Covers the properties of the Lebesgue measure and its existence.

Lebesgue Integral: Definition and Properties

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

Advanced analysis II

Covers Jordan-measurable sets, Riemann-integrability, and function continuity on compact sets.

Riemann Integral: Properties and Characterization

Explores the properties and characterization of the Riemann integral on different sets and measurable sets.

Advanced Analysis II: Consequences of Double Integrals

Explores the consequences of double integrals, including compact sets and continuity.

Analysis: Measure and Integration

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

Sigma Fields: Definition and Examples

Covers the concept of sigma fields and their role in probability theory.

Analysis IV: Measurable Sets and Functions

Introduces measurable sets, functions, and the Cantor set properties, including ternary development of numbers.

Analysis IV: Measurable Sets and Properties

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

Measurable Sets: Countable Additivity

Explores the countable additivity of measurable sets and the properties of sigma algebra, highlighting the significance of understanding measurable functions in analysis.

Measure Spaces: Integration and Inequalities

Covers measure spaces, integration, Radon-Nikodym property, and inequalities like Jensen, Hölder, and Minkowski.