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Cambridge Studies in Advanced Mathematics Ser.: Real Analysis and Probability by R. M. Dudley (2002, Trade Paperback)
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Real Analysis and Probability, Paperback by Dudley, R. M., ISBN 0521007542, ISBN-13 9780521007542, Brand New, Free shipping in the US This is a reissue of textbook covering graduate level courses in probability theory and real analysis, each conceived as a one-semester course. Dudley (Massachusetts Institute of Technology), in an effort to make the text self-contained, has added a treatment of the Stone- Weierstrass theorem. Annotation c. Book News, Inc., Portland, OR ()
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About this product
Product Identifiers
PublisherCambridge University Press
ISBN-100521007542
ISBN-139780521007542
eBay Product ID (ePID)1888298
Product Key Features
Number of Pages566 Pages
LanguageEnglish
Publication NameReal Analysis and Probability
Publication Year2002
SubjectFunctional Analysis, Probability & Statistics / General, Mathematical Analysis
FeaturesRevised
TypeTextbook
AuthorR. M. Dudley
Subject AreaMathematics
SeriesCambridge Studies in Advanced Mathematics Ser.
FormatTrade Paperback
Dimensions
Item Height1.1 in
Item Weight27.3 Oz
Item Length9.7 in
Item Width6.1 in
Additional Product Features
Edition Number2
Intended AudienceScholarly & Professional
LCCN2002-073698
Reviews'What makes the book special ... is the care and scholarship with which the material is treated, and the choice of additional topics ... not usually covered in first year graduate courses.' Mathematical Reviews, "A marvelous work which will soon become a standard text in the field for both teaching and reference...a complete and pedagogically perfect presentation of both the necessary preparatory material of real analysis and the proofs througout the text. Some of the topics and proofs are rarely found in other textbooks." Proceedings of the Edinburgh Mathematical Society, 'Careful, scholarly, and stimulating. It would be a pleasure to teach a mathematically-oriented graduate-level course from this text.' Short Book Reviews of the ISI, 'The book serves as a clear, rigorous, and complete introduction to modern probability theory using methods of mathematical analysis, and a description of relations between the two fields … it could be very useful for students interested in learning both topics, it can also serve as complementary reading to standard lectures. Teachers preparing their graduate level courses can use the book as an excellent, rigorously written and complete source.' EMS Newsletter, 'What makes the book special ... is the care and scholarship with which the material is treated, and the choice of additional topics ... not usually covered in first year graduate courses.'Mathematical Reviews, 'What makes the book special … is the care and scholarship with which the material is treated, and the choice of additional topics … not usually covered in first year graduate courses.'Mathematical Reviews, 'The book serves as a clear, rigorous, and complete introduction to modern probability theory using methods of mathematical analysis, and a description of relations between the two fields ... it could be very useful for students interested in learning both topics, it can also serve as complementary reading to standard lectures. Teachers preparing their graduate level courses can use the book as an excellent, rigorously written and complete source.'EMS Newsletter, 'A marvellous work which will soon become a standard text in the field for both teaching and reference … a complete and pedagogically perfect presentation of both the necessary preparatory material of real analysis and the proofs throughout the text. Some of the topics and proofs are rarely found in other textbooks.' Proceedings of the Edinburgh Mathematical Society, 'What makes the book special … is the care and scholarship with which the material is treated, and the choice of additional topics … not usually covered in first year graduate courses.' Mathematical Reviews, 'A marvellous work which will soon become a standard text in the field for both teaching and reference ... a complete and pedagogically perfect presentation of both the necessary preparatory material of real analysis and the proofs throughout the text. Some of the topics and proofs are rarely found in other textbooks.' Proceedings of the Edinburgh Mathematical Society
Dewey Edition21
Series Volume NumberSeries Number 74
IllustratedYes
Dewey Decimal515
Edition DescriptionRevised edition
Table Of Content1. Foundations: set theory; 2. General topology; 3. Measures; 4. Integration; 5. Lp spaces: introduction to functional analysis; 6. Convex sets and duality of normed spaces; 7. Measure, topology, and differentiation; 8. Introduction to probability theory; 9. Convergence of laws and central limit theorems; 10. Conditional expectations and martingales; 11. Convergence of laws on separable metric spaces; 12. Stochastic processes; 13. Measurability: Borel isomorphism and analytic sets; Appendixes: A. Axiomatic set theory; B. Complex numbers, vector spaces, and Taylor's theorem with remainder; C. The problem of measure; D. Rearranging sums of nonnegative terms; E. Pathologies of compact nonmetric spaces; Indices.
SynopsisThis classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, general topology, measure theory, integration, an introduction to functional analysis in Banach and Hilbert spaces, convex sets and functions and measure on topological spaces. The second half introduces probability based on measure theory, including laws of large numbers, ergodic theorems, the central limit theorem, conditional expectations and martingale's convergence. A chapter on stochastic processes introduces Brownian motion and the Brownian bridge. The edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution., This classic textbook, now reissued, offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The new edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution., This classic graduate textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The comprehensive historical notes have been further amplified for this edition, and a number of new exercises have been added, together with hints for solution.
LC Classification NumberQA300.D83 2002
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