Unit · year 4
MU-404 · Measure-Theoretic Probability
Threads chance5 theorems
Probability rebuilt on measure theory, up to the central limit theorem and martingales.
Theorems in this unit
T-131
The Borel–Cantelli lemmas
When infinitely many events occur, almost surely or not.
T-132
The strong law of large numbers
Sample means converge almost surely to the mean.
T-133
The central limit theorem
Sums of independent variables are asymptotically Gaussian.
T-134
Conditional expectation as projection
Conditioning is orthogonal projection in L2.
T-135
The martingale convergence theorem
A bounded martingale converges almost surely.