Notes for Statistics 600
References
- Why bother with measure-theoretic probability?
- 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.
- Hilbert spaces
- Densities and conditioning
- Product spaces and independence
- Conditional distributions
- Martingale et al
- Convergence in distribution
- Fourier methods
- Exponential tails and the law of the iterated logarithm
- Martingale CLTs and Brownian motion
Appendices
- Measures and integrals
- Inequalities
- Riesz representation
- Existence of conditional distributions (disintegrations)