Re: Axiom of Choice & Lebesgue Measure Problem

From: Tim Ball (tb_at_timball.net)
Date: 08/26/04 

Date: Thu, 26 Aug 2004 14:00:03 +0000 (UTC)

Mike Carroll wrote:

>Bas van Fraassen in his "Quantum Mechanics: An Empiricist View"
>mentions what he calls Lebesgue's "Measure Problem", which has to do
>with whether a measure on all subsets of a set can satisfy certain
>conditions (p.54). He then goes on to say that "... if the Axiom of
>Choice is true, Lebesgue's 'Measure Problem' has no solution".
>
>He does not go into the proof of this, though, instead referring the
>reader to G. Moore's 1982 monograph "Zermelo's Axiom of Choice."
>
>Moore's book is out of print, with not even any used copies available
>at Amazon. Does anybody know of any other sources, preferably more
>recent, that discuss the relationship between AC and Lebesgue's
>Measure Problem?
>
>Thanks.
>
>Mike Carroll
>Oro Valley, AZ
>
>
Try Fremlin's Measure Theory, esp. Volume 5.
http://www.essex.ac.uk/maths/staff/fremlin/mt.htm

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