Israel Journal of Mathematics

, Volume 48, Issue 1, pp 48–56

A mathematical proof of S. Shelah’s theorem on the measure problem and related results

  • Jean Raisonnier

DOI: 10.1007/BF02760523

Cite this article as:
Raisonnier, J. Israel J. Math. (1984) 48: 48. doi:10.1007/BF02760523


Recently, S. Shelah proved that an inaccessible cardinal is necessary to build a model of set theory in which every set of reals is Lebesgue measurable. We give a simpler and metamathematically free proof of Shelah's result. As a corollary, we get an elementary proof of the following result (without choice axiom): assume there exists an uncountable well ordered set of reals, then there exists a non-measurable set of reals. We also get results about Baire property,Kσ-regularity and Ramsey property.

Copyright information

© Hebrew University 1984

Authors and Affiliations

  • Jean Raisonnier
    • 1
  1. 1.UER 47Université Paris VIParis Cedex 05France