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Measure-Theoretic Probability

Probability made rigorous — sigma-algebras and measures, random variables as measurable maps, expectation as a Lebesgue integral, conditional expectation as an L^2 projection, and the limit theorems (LLN, CLT, extreme value) that underpin risk.

📚 13 lessons⏱ ~1.7 hours∑ Server-rendered mathematics

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What you'll learn

  • ✓Build probability on sigma-algebras and measures, with filtrations as information
  • ✓Treat expectation as a Lebesgue integral and use the convergence theorems
  • ✓Define and compute conditional expectation as an L^2 projection — the core of martingales
  • ✓Distinguish the modes of convergence and state the LLN and CLT precisely
  • ✓Model dependence and tail risk with the multivariate normal, copulas, and extreme value theory

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