Measure theory

Related lectures (32)

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

Covers independence between random variables and product measures in probability theory.

Explores the construction of measures, focusing on positive functionals and their properties in measure theory.

Covers the Lebesgue integration of simple functions and the approximation of nonnegative functions from below using piecewise constant functions.

Covers the fundamentals of probability measures, properties, examples, Lebesgue measure, and terminology related to probability spaces and events.

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

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

Covers convergence theorems and integrable functions, including the Lebesgue integral and Borel-Cantelli sets.

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

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