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Smooth inequality measurement: Approximation theorems

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  • Le Breton, Michel
  • Peluso, Eugenio

Abstract

The main purpose of this paper is to prove that smoothness is not a restrictive assumption in inequality measurement as any inequality measure (preorder) can be approximated in a well defined sense by a smooth inequality measure (preorder).

Suggested Citation

  • Le Breton, Michel & Peluso, Eugenio, 2010. "Smooth inequality measurement: Approximation theorems," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 405-415, July.
    • Handle: RePEc:eee:mateco:v:46:y:2010:i:4:p:405-415
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    References listed on IDEAS

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    1. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    2. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, vol. 38(6), pages 791-815, November.
    3. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    4. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    5. Le Breton, Michel, 1987. "Stochastic dominance: A bibliographical rectification and a restatement of whitmore's theorem," Mathematical Social Sciences, Elsevier, vol. 13(1), pages 73-79, February.
    6. Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
    7. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931, Decembrie.
    8. Frank K. Hwang & Uriel G. Rothblum, 1996. "Directional-Quasi-Convexity, Asymmetric Schur-Convexity and Optimality of Consecutive Partitions," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 540-554, August.
    9. Mas-Colell, Andreu, 1974. "Continuous and smooth consumers: Approximation theorems," Journal of Economic Theory, Elsevier, vol. 8(3), pages 305-336, July.
    10. Kannai, Yakar, 1974. "Approximation of convex preferences," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 101-106, August.
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    Cited by:

    1. Rolf Aaberge & Eugenio Peluso, 2011. "A Counting Approach for Measuring Multidimensional Deprivation," Working Papers 07/2011, University of Verona, Department of Economics.
    2. Aaberge, Rolf & Peluso, Eugenio & Sigstad, Henrik, 2019. "The dual approach for measuring multidimensional deprivation: Theory and empirical evidence," Journal of Public Economics, Elsevier, vol. 177(C), pages 1-1.
    3. Rolf Aaberge & Eugenio Peluso & Henrik Sigstad, 2015. "The dual approach for measuring. Multidimesional deprivation and poverty," Discussion Papers 820, Statistics Norway, Research Department.

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