Notes for Statistics 600


  1. Why bother with measure-theoretic probability?
  2. A modicum of measure theory (First 11 pages almost the same as version posted 11 Jan 99.)
    Correction: the measure P in Example 20 is supposed to be a probability measure, with total mass 1.
  3. Hilbert spaces
  4. Densities and conditioning
  5. Product spaces and independence
  6. Conditional distributions
  7. Martingale et al
  8. Convergence in distribution
  9. Fourier methods
  10. Exponential tails and the law of the iterated logarithm
  11. Martingale CLTs and Brownian motion


  1. Measures and integrals
  2. Inequalities
  3. Riesz representation
  4. Existence of conditional distributions (disintegrations)