Lectures related to Optional Stopping Theorem: Proof and Applications

Explains compression and Kraft inequality in codes and sequences.

Covers the long exact sequence of relative homology groups and chain complexes.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Covers the properties and applications of the Fourier transform and its relation to Heisenberg's uncertainty principle.

Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.

Covers the concept of Doob's martingale and its properties, including integrability and convergence theorem.

Explores martingales, adaptability, and stopping times in stochastic processes.

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

Covers conditional expectation, convergence of random variables, and the strong law of large numbers.