Analysis and Probability
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Analysis and Probability

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Description

Probability theory is a rapidly expanding field and is used in many areas of science and technology. Beginning from a basis of abstract analysis, this mathematics book develops the knowledge needed for advanced students to develop a complex understanding of probability. The first part of the book systematically presents concepts and results from analysis before embarking on the study of probability theory. The initial section will also be useful for those interested in topology, measure theory, real analysis and functional analysis. The second part of the book presents the concepts, methodology and fundamental results of probability theory. Exercises are included throughout the text, not just at the end, to teach each concept fully as it is explained, including presentations of interesting extensions of the theory. The complete and detailed nature of the book makes it ideal as a reference book or for self-study in probability and related fields.
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Product details

  • Hardback | 404 pages
  • 154.94 x 231.14 x 33.02mm | 793.78g
  • United States
  • English
  • 0124016650
  • 9780124016651

Table of contents

Chapter 1: Elements of Set Theory Chapter 2: Topological Preliminaries Chapter 3: Measure Spaces Chapter 4: The Integral Chapter 5: Measures on Product -algebras Chapter 6: Elementary Notions in Probability Theory Chapter 7: Distribution Functions and Characteristic Functions Chapter 8: Probabilities on Metric Spaces Chapter 9: Central Limit Problem Chapter 10: Sums of Independent Random Variables Chapter 11: Conditioning Chapter 12: Ergodicity, Mixing and Stationarity
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Review Text

"...The subject of this book is modern probability theory and it gives a full self-contained presentation of fundamental results within the area.it presents the theory of probability from a measure-theoretic point of view." --MathSciNet, Analysis and Probability

"This monograph is a self-contained and compactly written text book on probability theory for graduate students.the textbook gives a rigorous.presentation of the fundamental results in probability theory with an emphasis on the interaction between analysis and probability."-- Zentralblatt MATH, 1278.60002 "Spataru presents a probability theory text for graduate students who have a solid background in abstract analysis, which is required because he develops probability theory from a measure-theoretic perspective."-- Reference & Research Book News, October 2013
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Review quote

"...The subject of this book is modern probability theory and it gives a full self-contained presentation of fundamental results within the area...it presents the theory of probability from a measure-theoretic point of view."--MathSciNet, Analysis and Probability

"This monograph is a self-contained and compactly written text book on probability theory for graduate students...the textbook gives a rigorous...presentation of the fundamental results in probability theory with an emphasis on the interaction between analysis and probability."--Zentralblatt MATH, 1278.60002 "Spataru presents a probability theory text for graduate students who have a solid background in abstract analysis, which is required because he develops probability theory from a measure-theoretic perspective."--Reference & Research Book News, October 2013
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