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Measure Theory and Probability
The main goal of this Handbook is to survey measure theory with its many different branches and its relations with other areas of mathematics. Mostly aggregating many classical branches of measure theory the aim of the Handbook is also to cover new fields, approaches and applications which support the idea of "measure" in a wider sense, e. Although chapters are written of surveys in the various areas they contain many special topics and challenging problems valuable for experts and rich sources of inspiration. Mathematicians from other areas as well as physicists, computer scientists, engineers and econometrists will find useful results and powerful methods for their research. The reader may find in the Handbook many close relations to other mathematical areas: real analysis, probability theory, statistics, ergodic theory, functional analysis, potential theory, topology, set theory, geometry, differential equations, optimization, variational analysis, decision making and others.
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.
Measure 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.
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.