## A First Look at Rigorous Probability TheoryThis textbook is an introduction to probability theory using measure theory. It is designed for graduate students in a variety of fields (mathematics, statistics, economics, management, finance, computer science, and engineering) who require a working knowledge of probability theory that is mathematically precise, but without excessive technicalities. The text provides complete proofs of all the essential introductory results. Nevertheless, the treatment is focused and accessible, with the measure theory and mathematical details presented in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects. In this new edition, many exercises and small additional topics have been added and existing ones expanded. The text strikes an appropriate balance, rigorously developing probability theory while avoiding unnecessary detail. |

### Other editions - View all

### Common terms and phrases

A₁ absolutely continuous aperiodic Borel-measurable bounded Brownian motion Central Limit Theorem characteristic function collection Compute consider continuity of probabilities Convergence Theorem converges weakly Corollary countably additive defined definition density discrete disjoint E(Xn E(Xo equal equation equivalence event Exercise exists expected value finite mean finite-dimensional distributions follows Furthermore given Hence Hint implies inequality inf{n infinite integral interval Intuitively large numbers Lebesgue measure Lemma Let X1 lim inf lim sup limn linearity Markov chain martingale mathematical measure theory monotone convergence theorem non-negative o-algebra P(An P(lim P(Xn probability measure probability theory probability triple proof of Theorem Proposition Prove random walk real numbers result satisfied Section summary semialgebra sequence Similarly simple random variable simple symmetric random stationary distribution stochastic process submartingale subsets Suppose symmetric random walk transition probabilities Var(X Var(Y variance weak convergence X₁ µ(dx