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  1. Xref: sparky sci.math:17543 sci.physics:21942
  2. Path: sparky!uunet!news.claremont.edu!nntp-server.caltech.edu!allenk
  3. From: allenk@ugcs.caltech.edu (Allen Knutson)
  4. Newsgroups: sci.math,sci.physics
  5. Subject: Banach-Tarski (_NOT_ Re: Bayes' theorem and QM)
  6. Date: 31 Dec 1992 07:43:58 GMT
  7. Organization: California Institute of Technology, Pasadena
  8. Lines: 12
  9. Message-ID: <1hu8buINN8ve@gap.caltech.edu>
  10. References: <1992Dec24.101452.16194@oracorp.com> <1ht1arINNf8a@chnews.intel.com> <C03Er1.6wz@netnews.jhuapl.edu> <1992Dec30.225955.29902@news2.cis.umn.edu>
  11. NNTP-Posting-Host: torment.ugcs.caltech.edu
  12.  
  13. charlie@umnstat.stat.umn.edu (Charles Geyer) writes, under a wholly
  14. inappropriate subject line:
  15.  
  16. >If you think that every "real world" set should be measurable, and hence
  17. >Lebesgue theory is a waste of time, then you object to more of classical
  18. >mathematics than just the axiom of choice.
  19.  
  20. >Not so?
  21.  
  22. Not so. Solovay proved in 1970 that the axiom "All subsets of the reals are
  23. measurable" is consistent with ZF (obviously not with ZFC), under some
  24. standard large cardinal assumption. I think I have this right... Allen K.
  25.