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Preliminaries of Real Analysis, from Real Analysis with Economic Applications

In: Real Analysis with Economic Applications

Author

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  • Efe A. Ok

    (New York University)

Abstract

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.

Suggested Citation

  • Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters,in: Real Analysis with Economic Applications Princeton University Press.
  • Handle: RePEc:pup:chapts:8274-1
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    References listed on IDEAS

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    2. Wood, Peter John, 2010. "Climate Change and Game Theory: a Mathematical Survey," Working Papers 249379, Australian National University, Centre for Climate Economics & Policy.
    3. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2017. "Uniqueness of Nash Equilibrium in Continuous Weighted Potential Games," CSEF Working Papers 471, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 18 Jun 2017.
    4. Pierpaolo Battigalli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2017. "Mixed extensions of decision problems under uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(4), pages 827-866, April.
    5. repec:spr:etbull:v:5:y:2017:i:2:d:10.1007_s40505-016-0112-1 is not listed on IDEAS
    6. Gara Afonso & Ricardo Lagos, 2015. "Trade Dynamics in the Market for Federal Funds," Econometrica, Econometric Society, vol. 83, pages 263-313, January.
    7. Hota, Ashish R. & Garg, Siddharth & Sundaram, Shreyas, 2016. "Fragility of the commons under prospect-theoretic risk attitudes," Games and Economic Behavior, Elsevier, vol. 98(C), pages 135-164.
    8. Wang, Kun Tracy & Wang, Wanbin Walter, 2017. "Competition in the stock market with asymmetric information," Economic Modelling, Elsevier, pages 40-49.
    9. João Brogueira & Fabian Schütze, 2017. "Existence and uniqueness of equilibrium in Lucas’ asset pricing model when utility is unbounded," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 179-190, October.
    10. Chatterjee Kalyan & Krishna R. Vijay, 2012. "Uniquely Representing "A Preference for Uniformity"," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-36, January.
    11. K. Vela Velupillai, 2016. "Seven Kinds of Computable and Constructive Infelicities in Economics," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 219-239, November.
    12. Roman Gayduk & Sergey Nadtochiy, 2016. "Endogenous Formation of Limit Order Books: Dynamics Between Trades," Papers 1605.09720, arXiv.org, revised Jun 2017.
    13. repec:aea:aejmic:v:9:y:2017:i:2:p:263-94 is not listed on IDEAS
    14. Simone Cerreia Vioglio & Fabio Maccheroni & Massimo Marinacci, 2016. "Orthogonal Decompositions in Hilbert A-Modules," Working Papers 577, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    15. Andrei Barbos, 2016. "Dynamic Contracts with Random Monitoring," Working Papers 0416, University of South Florida, Department of Economics.
    16. Buechel, Berno & Hellmann, Tim & Pichler, Michael M., 2014. "The dynamics of continuous cultural traits in social networks," Journal of Economic Theory, Elsevier, pages 274-309.
    17. Miyamoto, Wataru & Nguyen, Thuy Lan & Sheremirov, Viacheslav, 2016. "The effects of government spending on real exchange rates: evidence from military spending panel data," Working Papers 16-14, Federal Reserve Bank of Boston.
    18. repec:kap:theord:v:83:y:2017:i:3:d:10.1007_s11238-017-9601-4 is not listed on IDEAS
    19. Yeon-Koo Che & Youngwoo Koh, 2016. "Decentralized College Admissions," Journal of Political Economy, University of Chicago Press, vol. 124(5), pages 1295-1338.
    20. K. Vela Velupillai, 2016. "Max Euwe's Set-Theoretic Observations on the Game of Chess — Introductory Notes," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 12(01), pages 21-28, March.
    21. Amaral, Pedro S. & Corbae, Dean & Quintin, Erwan, 2016. "A New Perspective on the Finance-Development Nexus," Working Paper 1629, Federal Reserve Bank of Cleveland, revised 13 Jun 2017.

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