Analysis 2: Properties and Integrability

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Related lectures (30)

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Change of Variables Theorem in the Plane

Explores the change of variables theorem in the plane, emphasizing boundedness and continuity of functions.

Lebesgue Integration: Cantor Set

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

Continuous Functions: Definitions and Criteria

Covers the definition and criteria for continuous functions and explores the intermediate value theorem.

Lebesgue Measure: Definition and Properties

Explores the Lebesgue outer measure, its properties, and applications in measure theory.

Lebesgue Measure and Fourier Analysis

Explores Lebesgue measure, Fourier analysis, PDE applications, and optimal transport in PDEs.

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.

Functions: Continuity and Derivability

Explores continuous and derivable functions on closed intervals.

Measure Theory: Properties and Integrability

Explores properties of null measure subsets, integrability criteria, and average value concepts.

Functions Composition: Continuity & Elements

Covers the composition of functions, continuity, and elementary functions, explaining the concept of continuity and the construction of elementary functions.

Calculus of Variations: Principles and Applications

Explores the principles and applications of calculus of variations, focusing on uniform boundedness and equi-integrability of Carathéodory integrands.