Abstract
Measure theory is that part of mathematics which is concerned with the attribution of weights of ‘measure’ to the subsets of some given set. Such a measure is required to satisfy a natural condition of additivity, that is that the measure of the union of disjoint sets should be equal to the sum of the measure of those sets. The fundamental problems of measure arise when one has to treat infinite sets or infinite unions of sets. It is perhaps not clear why such a tool should be of use in economics.
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Bibliography
Any standard text in measure theory such as Halmos (1971) will give the essential mathematical notions, and more specialized references are given in the bibliographies of the articles cited here.
Arrow, K.J. 1963. Social choice and individual values. 2nd ed. New York: Wiley.
Aumann, R.J. 1964. Markets with a continuum of traders. Econometrica 32: 39–50.
Debreu, G. 1970. Economies with a finite set of equilibria. Econometrica 38: 387–392.
Debreu, G. 1974. Excess demand functions. Journal of Mathematical Economics 1 (1): 15–21.
Dubins, I.E., and E.H. Spanier. 1961. How to cut a cake fairly. American Mathematical Monthly 1: 1–17.
Fishburn, P.C. 1970. Arrow’s impossibility theorem, concise proof and infinite voters. Journal of Economic Theory 2: 103–106.
Grandmont, J.M. 1977. Temporary general equilibrium theory. Econometrica 45 (3): 535–572.
Halmos, P.R. 1961. Measure theory. 7th ed. Princeton: Van Nostrand.
Hildenbrand, W. 1975. Distributions of agents characteristics. Journal of Mathematical Economics 2: 129–138.
Hildenbrand, W. 1983. On the law of demand. Econometrica 51 (4): 997–1020.
Kirman, A.P. 1982. Chapter 5: Measure theory with applications to economics. In Handbook of mathematical economics, ed. K.J. Arrow and M. Intriligator, vol. 1, 159–209.
Kirman, A.P., and K.J. Koch. 1986. Market excess demand in economies with identical preferences and co-linear endowments. Review of Economic Studies 53 (3): 457–464.
Mas-Colell, A. 1985. The theory of general economic equilibrium. Cambridge: Cambridge University Press.
Sonnenschein, H. 1973. Do Walras’s identity and continuity characterise the class of community excess demand functions. Journal of Economic Theory 6 (4): 345–354.
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Kirman, A.P. (2018). Measure Theory. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_1172
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DOI: https://doi.org/10.1057/978-1-349-95189-5_1172
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