Israel Journal of Mathematics

, Volume 48, Issue 1, pp 48–56 | Cite as

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

  • Jean Raisonnier


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,K σ-regularity and Ramsey property.


Measure Problem Infinite Subset Rapid Filter Inaccessible Cardinal Baire Property 
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Copyright information

© Hebrew University 1984

Authors and Affiliations

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

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