This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is 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 arguments and understand what they mean.A, ) (A.Bi) alt; oo. For each / in the set J^ := {i : M, 4, = 00} we must have XBi = 0, which implies that the set Wx := U^Bi is A.-negligible. ... For the SLLN problem there are several types of maximal inequality that could be used. I am fond of ... The inequality is but one example of a large class of results based on a simple principle.

Title | : | A User's Guide to Measure Theoretic Probability |

Author | : | David Pollard |

Publisher | : | Cambridge University Press - 2002 |

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