Dudley : Review: P. Billingsley, Convergence of probability measuresMeasure theory and integration are presented to undergraduates from the perspective of probability theory. The first chapter shows why measure theory is needed for the formulation of problems in probability, and explains why one would have been forced to invent Lebesgue theory had it not already existed to contend with the paradoxes of large numbers. The measure-theoretic approach then leads to interesting applications and a range of topics that include the construction of the Lebesgue measure on R [superscript n] metric space approach , the Borel-Cantelli lemmas, straight measure theory the Lebesgue integral. In this concise text, quite a few applications to probability are packed into the exercises. All in all, the text should make a useful reference for professionals and students. Skip to main content Skip to table of contents. Advertisement Hide.
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations , probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space , which assigns a measure taking values between 0 and 1, termed the probability measure , to a set of outcomes called the sample space. Any specified subset of these outcomes is called an event. Central subjects in probability theory include discrete and continuous random variables , probability distributions , and stochastic processes , which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion.
Probability PHI Learning books :
Measure Theory 1.1 : Definition and Introduction
Save extra with 3 Offers. Measure Theory And Probability by A. Basu Book Summary: This compact and well-received book, now in its second edition, is a skilful combination of measure theory and probability. For, in contrast to many books where probability theory is usually developed after a thorough exposure to the theory and techniques of measure and integration, this text develops the Lebesgue theory of measure and integration, using probability theory as the motivating force. A section is devoted to large sample theory of statistics, and another to large deviation theory in the Appendix. View Snapshot.