Émile Borel

Related lectures (11)

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

Covers the proof of unitary group uniqueness and spectral types.

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

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

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

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

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

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

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

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