Σ-algebra

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Related lectures (30)

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

Exponential Maps: Properties and Applications in Lie Groups

Covers the properties of the exponential map in Lie groups and their algebras, including smoothness and the relationship between subgroups and algebras.

Pareto Efficiency: Social Planner's Problem

Explains Pareto efficiency, social planner's problem, and optimal consumption allocation in complete markets.

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Probability Theory: Lecture 2

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

Measure Theory: Sets and Algebras

Covers measurability, independence of sets, sigma-algebras, cylinder sets, co-algebras, uniqueness, and extension of measures.

Discrete-Time Markov Chains: Definitions

Covers the definitions and state probabilities of discrete-time Markov chains.

Discrete-Time Markov Chains: Definitions

Covers the definitions and state probabilities of discrete-time Markov chains.

Stochastic Block Model

Covers the Stochastic Block Model and its application in community detection, exploring its mathematical formulation and challenges.

Integration on H_pxH and Arithmetic

Explores integration on H_pxH and arithmetic properties, including norms, structures, and polynomial factorization.

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Geometric Examples

Explores geometric examples related to linear applications in algebra.

Conditional Entropy and Data Compression Techniques

Discusses conditional entropy and its role in data compression techniques.

Linear Maps and the Duality Principle in Mathematics

Covers the duality principle in linear algebra and its implications in mathematics.

Reordering of Series, Power Series

Explores reordering series and the properties of power series for function representation.

Periodic Orbits of Hamiltonian Systems

Covers the theory of periodic orbits of Hamiltonian systems and the Conley-Zehnder index.

Calderbank-Steane-Shor Codes

Explores Calderbank-Steane-Shor codes, classical codes, error correction, CSS codes, and protecting states from errors.

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