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Efe A. Ok Real Analysis with Economic Applications (Hardback)
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Item specifics
- Condition
- Book Title
- Real Analysis with Economic Applications
- Title
- Real Analysis with Economic Applications
- ISBN-10
- 0691117683
- EAN
- 9780691117683
- ISBN
- 9780691117683
- Genre
- Business & Finance
- Subject
- Science Nature & Math
- Release Date
- 01/22/2007
- Release Year
- 2007
- Country/Region of Manufacture
- US
- Publication Year
- 2007
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Publication Name
- Real Analysis with Economic Applications
- Item Height
- 2.1in
- Item Length
- 9.5in
- Publisher
- Princeton University Press
- Item Width
- 6.5in
- Item Weight
- 43 Oz
- Number of Pages
- 832 Pages
About this product
Product Information
There are many mathematics textbooks on real analysis, but they focus on topics not readily helpful for studying economic theory or they are inaccessible to most graduate students of economics. Real Analysis with Economic Applications aims to fill this gap by providing an ideal textbook and reference on real analysis tailored specifically to the concerns of such students. The emphasis throughout is on topics directly relevant to economic theory. In addition to addressing the usual topics of real analysis, this book discusses the elements of order theory, convex analysis, optimization, correspondences, linear and nonlinear functional analysis, fixed-point theory, dynamic programming, and calculus of variations. Efe Ok complements the mathematical development with applications that provide concise introductions to various topics from economic theory, including individual decision theory and games, welfare economics, information theory, general equilibrium and finance, and intertemporal economics. Moreover, apart from direct applications to economic theory, his book includes numerous fixed point theorems and applications to functional equations and optimization theory. The book is rigorous, but accessible to those who are relatively new to the ways of real analysis. The formal exposition is accompanied by discussions that describe the basic ideas in relatively heuristic terms, and by more than 1,000 exercises of varying difficulty. This book will be an indispensable resource in courses on mathematics for economists and as a reference for graduate students working on economic theory.
Product Identifiers
Publisher
Princeton University Press
ISBN-10
0691117683
ISBN-13
9780691117683
eBay Product ID (ePID)
45102081
Product Key Features
Publication Name
Real Analysis with Economic Applications
Format
Hardcover
Language
English
Publication Year
2007
Type
Textbook
Number of Pages
832 Pages
Dimensions
Item Length
9.5in
Item Height
2.1in
Item Width
6.5in
Item Weight
43 Oz
Additional Product Features
Lc Classification Number
Hb135.O45 2007
Reviews
"This book is poised to be a standard reference. Its author gets high marks for care of execution and obvious devotion to, and command of, the topics." --Wei Xiong, Princeton University, "Important and commendable, this indispensable resource should be highly prized by all concerned with courses on mathematics for economists and by graduate students working on economic theory. Rarely do books meet such high aspirations and carry out their aims, yet this one certainly does. Well written in an engaging style and impressively researched in the requirements of graduate students of economics and finance, Real Analysis with Economic Applications is sure to become the definitive work for its intended audience. Real Analysis with Economic Applications with its large number of economics applications and variety of exercises represents the single most important mathematical source for students of economics applications and it will be the book, for a long time to come, to which they will turn with confidence, as well as pleasure, in all questions of economic applications." -- Current Engineering Practice, The book is intended as a textbook on real analysis for graduate students in economics. It is largely graduate level mathematics, and the students should have a solid undergraduate real analysis background. . . . The author's writing style is . . . in general quite attractive. The book should be quite successful for its intended purpose., Important and commendable, this indispensable resource should be highly prized by all concerned with courses on mathematics for economists and by graduate students working on economic theory. Rarely do books meet such high aspirations and carry out their aims, yet this one certainly does. Well written in an engaging style and impressively researched in the requirements of graduate students of economics and finance, Real Analysis with Economic Applications is sure to become the definitive work for its intended audience. Real Analysis with Economic Applications with its large number of economics applications and variety of exercises represents the single most important mathematical source for students of economics applications and it will be the book, for a long time to come, to which they will turn with confidence, as well as pleasure, in all questions of economic applications., "This very well written book displays its author's engaging style, and offers interesting questions between topics that make them entertaining to read through." --Darrell Duffie, Stanford University, author of Dynamic Asset Pricing Theory, "The book is intended as a textbook on real analysis for graduate students in economics. It is largely graduate level mathematics, and the students should have a solid undergraduate real analysis background. . . . The author's writing style is . . . in general quite attractive. The book should be quite successful for its intended purpose." --Gerald A. Heuer, Zentralblatt MATH, The book is intended as a textbook on real analysis for graduate students in economics. It is largely graduate level mathematics, and the students should have a solid undergraduate real analysis background. . . . The author's writing style is . . . in general quite attractive. The book should be quite successful for its intended purpose. ---Gerald A. Heuer, Zentralblatt MATH, Important and commendable, this indispensable resource should be highly prized by all concerned with courses on mathematics for economists and by graduate students working on economic theory. Rarely do books meet such high aspirations and carry out their aims, yet this one certainly does. Well written in an engaging style and impressively researched in the requirements of graduate students of economics and finance, Real Analysis with Economic Applications is sure to become the definitive work for its intended audience. Real Analysis with Economic Applications with its large number of economics applications and variety of exercises represents the single most important mathematical source for students of economics applications and it will be the book, for a long time to come, to which they will turn with confidence, as well as pleasure, in all questions of economic applications. -- Current Engineering Practice, "Because of its comprehensive coverage of the basic topics of real analysis that are of primary interest to economists, this is a much-needed contribution to the current selection of mathematics textbooks for students of economics, and it will be a good addition to any economist's library. It includes a large number of economics applications that will motivate students to learn the math, and its number and variety of exercises--forty to fifty in each chapter--is a further asset." --Susan Elmes, Columbia University, "The book is intended as a textbook on real analysis for graduate students in economics. It is largely graduate level mathematics, and the students should have a solid undergraduate real analysis background. . . . The author's writing style is . . . in general quite attractive. The book should be quite successful for its intended purpose."-- Gerald A. Heuer, Zentralblatt MATH, "The idea of doing such a math book directed toward graduate students of economics and finance is an excellent one. There are many students who are interested in this topic, and--until now--the existing math books have not directed their examples and exercises toward an economics approach." --Salih Neftci, City University of New York, "Important and commendable, this indispensable resource should be highly prized by all concerned with courses on mathematics for economists and by graduate students working on economic theory. Rarely do books meet such high aspirations and carry out their aims, yet this one certainly does. Well written in an engaging style and impressively researched in the requirements of graduate students of economics and finance, Real Analysis with Economic Applications is sure to become the definitive work for its intended audience. Real Analysis with Economic Applications with its large number of economics applications and variety of exercises represents the single most important mathematical source for students of economics applications and it will be the book, for a long time to come, to which they will turn with confidence, as well as pleasure, in all questions of economic applications."-- Current Engineering Practice, The book is intended as a textbook on real analysis for graduate students in economics. It is largely graduate level mathematics, and the students should have a solid undergraduate real analysis background. . . . The author's writing style is . . . in general quite attractive. The book should be quite successful for its intended purpose. -- Gerald A. Heuer, Zentralblatt MATH, Important and commendable, this indispensable resource should be highly prized by all concerned with courses on mathematics for economists and by graduate students working on economic theory. Rarely do books meet such high aspirations and carry out their aims, yet this one certainly does. Well written in an engaging style and impressively researched in the requirements of graduate students of economics and finance,Real Analysis with Economic Applicationsis sure to become the definitive work for its intended audience.Real Analysis with Economic Applicationswith its large number of economics applications and variety of exercises represents the single most important mathematical source for students of economics applications and it will be the book, for a long time to come, to which they will turn with confidence, as well as pleasure, in all questions of economic applications.
Table of Content
Preface xvii Prerequisites xxvii Basic Conventions xxix Part I: SET THEORY 1 Chapter A: Preliminaries of Real Analysis 3 A.1 Elements of Set Theory 4 A.1.1 Sets 4 A.1.2 Relations 9 A.1.3 Equivalence Relations 11 A.1.4 Order Relations 14 A.1.5 Functions 20 A.1.6 Sequences, Vectors, and Matrices 27 A.1.7* A Glimpse of Advanced Set Theory: The Axiom of Choice 29 A.2 Real Numbers 33 A.2.1 Ordered Fields 33 A.2.2 Natural Numbers, Integers, and Rationals 37 A.2.3 Real Numbers 39 A.2.4 Intervals and R 44 A.3 Real Sequences 46 A.3.1 Convergent Sequences 46 A.3.2 Monotonic Sequences 50 A.3.3 Subsequential Limits 53 A.3.4 Infinite Series 56 A.3.5 Rearrangement of Infinite Series 59 A.3.6 Infinite Products 61 A.4 Real Functions 62 A.4.1 Basic Definitions 62 A.4.2 Limits, Continuity, and Differentiation 64 A.4.3 Riemann Integration 69 A.4.4 Exponential, Logarithmic, and Trigonometric Functions 74 A.4.5 Concave and Convex Functions 77 A.4.6 Quasiconcave and Quasiconvex Functions 80 Chapter B: Countability 82 B.1 Countable and Uncountable Sets 82 B.2 Losets and Q 90 B.3 Some More Advanced Set Theory 93 B.3.1 The Cardinality Ordering 93 B.3.2* The Well-Ordering Principle 98 B.4 Application: Ordinal Utility Theory 99 B.4.1 Preference Relations 100 B.4.2 Utility Representation of Complete Preference Relations 102 B.4.3* Utility Representation of Incomplete Preference Relations 107 Part II: ANALYSIS ON METRIC SPACES 115 Chapter C: Metric Spaces 117 C.1 Basic Notions 118 C.1.1 Metric Spaces: Definition and Examples 119 C.1.2 Open and Closed Sets 127 C.1.3 Convergent Sequences 132 C.1.4 Sequential Characterization of Closed Sets 134 C.1.5 Equivalence of Metrics 136 C.2 Connectedness and Separability 138 C.2.1 Connected Metric Spaces 138 C.2.2 Separable Metric Spaces 140 C.2.3 Applications to Utility Theory 145 C.3 Compactness 147 C.3.1 Basic Definitions and the Heine-Borel Theorem 148 C.3.2 Compactness as a Finite Structure 151 C.3.3 Closed and Bounded Sets 154 C.4 Sequential Compactness 157 C.5 Completeness 161 C.5.1 Cauchy Sequences 161 C.5.2 Complete Metric Spaces: Definition and Examples 163 C.5.3 Completeness versus Closedness 167 C.5.4 Completeness versus Compactness 171 C.6 Fixed Point Theory I 172 C.6.1 Contractions 172 C.6.2 The Banach Fixed Point Theorem 175 C.6.3* Generalizations of the Banach Fixed Point Theorem 179 C.7 Applications to Functional Equations 183 C.7.1 Solutions of Functional Equations 183 C.7.2 Picard's Existence Theorems 187 C.8 Products of Metric Spaces 192 C.8.1 Finite Products 192 C.8.2 Countably Infinite Products 193 Chapter D: Continuity I 200 D.1 Continuity of Functions 201 D.1.1 Definitions and Examples 201 D.1.2 Uniform Continuity 208 D.1.3 Other Continuity Concepts 210 D.1.4* Remarks on the Differentiability of Real Functions 212 D.1.5 A Fundamental Characterization of Continuity 213 D.1.6 Homeomorphisms 216 D.2 Continuity and Connectedness 218 D.3 Continuity and Compactness 222 D.3.1 Continuous Image of a Compact Set 222 D.3.2 The Local-to-Global Method 223 D.3.3 Weierstrass' Theorem 225 D.4 Semicontinuity 229 D.5 Applications 237 D.5.1* Caristi's Fixed Point Theorem 238 D.5.2 Continuous Representation of a Preference Relation 239 D.5.3* Cauchy's Functional Equations: Additivity on Rn 242 D.5.4* Representation of Additive Preferences 247 D.6 CB(T) and Uniform Convergence 249 D.6.1 The Basic Metric Structure of CB(T) 249 D.6.2 Uniform Convergence 250 D.6.3* The Stone-Weierstrass Theorem and Separability of C(T) 257 D.6.4* The Arzelagrave;-Ascoli Theorem 262 D.7* Extension of Conti
Copyright Date
2007
Topic
Finance / General, Economics / Theory, Mathematical Analysis
Lccn
2006-049378
Dewey Decimal
330.1/51
Intended Audience
College Audience
Dewey Edition
22
Illustrated
Yes
Genre
Business & Economics, Mathematics
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