Title: A user's guide to measure theoretic probability /
Authors: Pollard, David, 1950-
Publisher: Cambridge University Press,
Year: 2002
Subjects: Probabilities; Measure theory.; Eminent domain
Abstract: This text is not just a presentation of mathematical theory, but also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguements and understand what they mean.
Contents: Chapter 1. Motivation -- Ch. 2. A modicum of measure theory -- Ch. 3. Densities and derivatives -- Ch. 4. Product spaces and independence -- Ch. 5. Conditioning -- Ch. 6. Martingale et al. -- Ch. 7. Convergence in distribution -- Ch. 8. Fourier transforms -- Ch. 9. Brownian motion -- Ch. 10. Representations and couplings -- Ch. 11. Exponential tails and the law of the iterated logarithm -- Ch. 12. Multivariate normal distributions -- App. A. Measures and integrals -- App. B. Hilbert spaces -- App. C. Convexity -- App. D. Binomial and normal distributions -- App. E. Martingales in continuous time -- App. F. Disintegration of measures.