Émile Borel

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Related lectures (11)

Lebesgue Integration: Cantor Set

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

Unitary Group and Spectral Types

Covers the proof of unitary group uniqueness and spectral types.

Probability Convergence

Explores probability convergence, discussing conditions for random variable sequences to converge and the uniqueness of convergence.

Analysis IV: Convergence Theorems and Integrable Functions

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

Borel-Cantelli Lemma & Law of Large Numbers

Introduces the Borel-Cantelli lemma and the laws of large numbers.

Convergence in Law: Theorem and Proof

Explores convergence in law for random variables, including Kolmogorov's theorem and proofs based on probability lemmas.

Spectral Decomposition of Unbounded Operators

Explores the spectral decomposition of non-bounded operators and presents the spectral theorem for self-adjoint non-bounded operators.

Dynamics on Homogeneous Spaces and Number Theory

Covers dynamical systems on homogeneous spaces and their interactions with number theory.

Nonlinear Bourgain's Projection Theorem

Explores a nonlinear version of Bourgain's Projection Theorem and its diverse applications in mathematics.

Stochastic Calculus: Lecture 1

Covers the essentials of probability, algebras, and conditional probability, including the Borel o-algebra and Poisson processes.

Probability Measures and Random Variables

Covers the Caratheodory extension theorem, uniqueness and existence of probability measures, Bernoulli random variables, and spaces of random variables.

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