[FOM] Category and Measure

[joeshipman@aol.com]

***
-----Original Message-----
From: Bill Taylor <W.Taylor at math.canterbury.ac.nz>


That is, we know a subset of [0,1] might have "null category" (meagre), 
or
"full category" (co-meagre); but can things in between be sensibly 
defined?
***

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.

-- JS
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