Abstract
The major motivation of earlier studies on large markets with pure competition was always the aspiration for a well interpretable verification of F.Y.Edgeworth’s conjecture concerning the Core-Walras equivalence. Consequently it is our natural desire to investigate this classical conjecture within the model installed here and its intrinsic logic. Since our approach differs from other contributions to this theme we have to deduce the necessary notions before a verification of the equivalence result can be probed.
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References Concerning Chapter I - III
ARMSTRONG, T.E.: Remarks Related to Finitely Additive Exchange Economies, Proceedings Indianapolis 1984, Lecture Notes in Economics and Math. Systems 244 (1985).
ARMSTRONG, T.E. and RICHTER, M.K.: The Core Walras Equivalence, Journal of Economic Theory 33 (1984), 116–151.
ARMSTRONG, T.E. and RICHTER, M.K.: Existence of Nonatomic Core-Walras Allocations, Journal of Economic Theory 38 (1986), 137–159.
ARMSTRONG, T.E.: Stone Spaces of Algebras of Arithmetic Sequences, Research Report, University of Minnesota 1977.
AUMANN, R.J.: Markets with a Continuum of Traders, Econometrica 32 (1964), 39–50.
AUMANN, R.J. and SHAPLEY, L.S.: Values of Non-Atomic Games, Princeton 1974.
BRUNK, H.D.: Stone Spaces in Probability, Oregon University, Dept. of Statistics, Technical Report No. 52 (1976).
DEBREU, G.: On a Theorem of Scarf, Review of Economic Studies 30 (1963), 177–180.
DEBREU, G.: Theory of Value, New York 1959.
EDGEWORTH, F.Y.: Mathematical Psychics, London 1881.
HALMOS, P.R.: Measure Theory, New York, Toronto, Melbourne 1973.
HARDY, G.H. and WRIGHT, E.M.: An Introduction to the Theory of Numbers, Oxford 1960.
HILDENBRAND, W.: Core and Equilibria of a Large Economy, Princeton 1974.
HLAWKA, E.: Theorie der Gleichverteilung, Mannheim, Wien, Zürich 1979.
KLEIN, C. and ROLEWICZ, S.: On Riemann Integration of Functions with Values in Topological Linear Spaces, Studia Math. 80 (1984), 109–118.
KLEIN, C.: Invariance Properties of the Banach Algebra of Darboux Integrable Functions, Proc. Karlsruhe 1983, ed. G.Hammer and D.Pallaschke, Lecture Notes in Economics and Math. Systems 226 (1984), 382–411.
KLEIN, C.: Arzela-Ascoli’s Theorem for Riemann Integrable Functions on Compact Spaces, Manuscripta Math. 55 (1986), 403–418.
KLEIN, C.: On Functions whose Improper Riemann Integral is Absolutely Convergent, Studia Math. 85 (1987), 247–255.
KLEIN, C.: Atomless Economies with Countably Many Agents, Proc. of the Seminar on Game Theory, Bonn-Hagen 1978, ed. O.Moeschlin and D.Pallaschke, Amsterdam 1979.
KLEIN, C.: Closed Subsets of the Set of Monotone Preferences, Methods of Operations Research 41 (1981), 301–304.
KLEIN, C.: The Observation of a Deterministic Microeconomic Model of a Large Economy, Proc. of the Seminar on Game Theory, Bonn - Hagen 1980, ed. O.Moeschlin and D.Pallaschke, Amsterdam 1981 217–231.
KLEIN, C.: Finitely Additive Measures on Subsets of Compact Spaces, Meth. of Operations Research 46 (1983), 297–305.
KRICKEBERG, K.: Strong Mixing Properties of Markov Chains with Infinite Invariant Measure, Proc. Fifth Berkeley Symp. Math. Stat. Probability 1965 Vol. II, Part 2, 431–466, Berkeley and Los Angeles, University of California Press, 1967.
KUIPERS, L. and NIEDERREITER, H.: Uniform Distribution of Sequences, New York, London, Sydney 1974.
KURATOWSKY, K.: Topology I, New York 1966.
LOS, J.: On the Axiomatic Treatment of Probability, Coll. Math. 3 (1955), 125–137.
MAS COLELL, A.: The Theory of General Economic Equilibrium, Cambridge 1985.
MORISHIMA, M.: Walras’ Economics, Cambridge 1978.
NOELLE-NEUMANN, E.: Umfragen in der Massengesellschaft, Reinbeck 1963.
PALLASCHKE, D.: Markets with Countably Many Traders, Journal of Applied Math. and Comp. 4 (1978), 201–212.
ROLEWICZ, S.: Metric Linear Spaces, Warszawa 1972 and 1984, Dordrecht, Boston, Lancaster 1984.
SCARF, H.: An Analysis of Markets with a Large Number of Participants, Recent Advances in Game Theory, The Princeton University Conference, 1962, 127–155.
SEMADENI, Z.: Banach Spaces of Continuous Functions I, Warszawa 1971.
SEMADENI, Z.: Describing q-Adic Solenoids as Maximal Ideal Spaces of Subalgebras of C(R), Functiones et Approximatio XVII, Adam Mickiewicz University Press, Poznan 1987, 97–106.
SIKORSKI, R.: Boolean Algebras, Berlin, Heidelberg, New York 1969.
VLADIMIROV, D.A.: Bool’sche Algebren, Berlin 1972.
WALRAS, L.: Elements d’economie politique pure, Lausanne 1874.
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Klein, C. (1988). Core and Walras Allocations. In: A Static Microeconomic Model of Pure Competition. Lecture Notes in Economics and Mathematical Systems, vol 306. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46639-7_4
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DOI: https://doi.org/10.1007/978-3-642-46639-7_4
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