Optional Stopping Theorem: Proof and Applications

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Covers the Zig Zag Lemma and the long exact sequence of relative homology.

Explores three stopping theorems in martingales and Brownian motion.

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Covers examples of direct and indirect proofs in mathematics.

Explores differentiating under the integral sign and continuity of functions in integrals.

Covers proof techniques including direct proof, contraposition, contradiction, cases, and counterexample.

Explores the convergence of martingales under specific conditions and previews upcoming topics on martingale theorems and inequalities.

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

Explores the concept of universal coating through detailed proofs and examples, emphasizing uniqueness and significance.

Explores the proof of measure concentration using Laplace transform methods and demonstrates its application through examples and propositions.