[FOM] Category and Measure
joeshipman at aol.com
Fri Sep 21 15:26:09 EDT 2007
From: Bill Taylor <W.Taylor at math.canterbury.ac.nz>
That is, we know a subset of [0,1] might have "null category" (meagre),
"full category" (co-meagre); but can things in between be sensibly
The obvious place to start is to call subintervals of [0,1] of length c
"category c" and meager sets "category 0" and define the disjoint union
of two subsets of [0,1] of categories a and b to have category a+b.
If you try to extend this to cover countable disjoint unions and
complementation you run into trouble, because then you get a full sigma
algebra and can obtain a null set whose complement is meager. But
finite unions and complementation should be OK.
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