Measure and Probability

Covering the fundamentals of measure theory and probability theory, this title begins with the construction of Lebesgue measure via Caratheodory's outer measure approach and goes on to discuss integration and standard convergence theorems.

List of contents

Probabilities and Measures. Integration. Random Variables. Probability Measures on Product Spaces. Characteristics and Convergences. Markov Chains. Some Analysis. Appendix. Tables. References. Index.

About the author

Siva Athreya

Summary

This book covers the fundamentals of measure theory and probability theory. Topics include the construction of Lebesgue measure via Caratheodory’s outer measure approach; integration and standard convergence theorems; complex measures, Lp spaces, Radon–Nikodym theorem, and the Riesz representation theorem.

Additional text

This textbook is suitable for a one-semester course on measure theory and probability for beginning graduate students in mathematics, probability and statistics. It can also be used as a textbook for advanced undergraduate students in mathematics … The topics are well selected to meet the needs of students who are interested in graduate studies in areas related to analysis, probability, stochastic processes and statistics … This makes the book student-friendly. A motivated student can use it by him- or herself to learn the topics well.
—Yimin Xiao, Mathematical Reviews, 2010

Product details

• Authors: ATHREYA, Siva Athreya, Siva (Indian Academy of Sciences Athreya, Siva (Universities Press Athreya, Siva Sunder Athreya, Athreya Siva, V. S. Sunder, V. S. (Institute of Mathematical Sciences Sunder, Sunder V. S.
• Publisher: Taylor & Francis Ltd.
• Languages: English
• Product format: Paperback / Softback
• Released: 30.09.2018
• EAN: 9781138114180
• ISBN: 978-1-138-11418-0
• No. of pages: 232
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; MATHEMATICS / General, MATHEMATICS / Functional Analysis, MATHEMATICS / Probability & Statistics / Bayesian Analysis, Probability & statistics, Calculus & mathematical analysis, Probability and statistics, Calculus and mathematical analysis