Lectures related to Base Point Change in Fiber: Connectivity and Conjugation

Proof of Convergence Rate Theorem

Covers the proof of the convergence rate theorem, emphasizing the correction of a missing factor sqrt{pi_j} in the proof.

Sparsest Cut: ARV Theorem

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Proof of Surjectivity

Covers the proof of surjectivity, demonstrating the existence of connections between elements through arcs.

Implicit Functions: Unique Solutions and Class C Functions

Covers the proof of the theorem of implicit functions and the concept of class C functions.

Analysis IV: Measurable Sets and Properties

Covers the concept of outer measure and properties of measurable sets.

Subgroups Criteria: Propositions and Examples

Covers the criteria for subgroups and provides examples and proofs.

Markov Chains Decomposition

Covers Markov chains decomposition, LLN proof, Inventory Model application, and average costs.

Convergence in Law: Theorem and Proof

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