FOM: Cantor's theorem of little interest in constructive math

Kanovei kanovei at
Wed Feb 14 14:54:58 EST 2001

>From: Ayan <amah8857 at>

>there are more Lebesgue measurable sets than Borel 
measurable using the completeness of L-measure and the cantor set. Does 
anybody know of any argument to bypass the obvious use of cardinality here

One easily obtains LM but not Borel subset of R using axiom of 
choice. If AC is not permitted the notion of Borel set needs to 
be adjusted (otherwise all sets can be Borel). 


More information about the FOM mailing list