[FOM] Category and Measure
joeshipman@aol.com
joeshipman at aol.com
Mon Sep 17 21:34:09 EDT 2007
***
----Original Message-----
From: James Hirschorn <James.Hirschorn at univie.ac.at>
But perhaps the following example is relevant:
Let a_n and b_n be sequences of real numbers, indexed by the natural
numbers.
Call them *similar* if one can be obtained from the other by
translation and
dilation, i.e.
a_n = r X b_n + s for all n, for some fixed reals r and s.
Consider the following statement: "Given a bounded sequence a_n of
reals,
every Borel set of reals that is not 'small' contains a sequence
similar to
a_n".
This statement with 'small' interpreted as meager is a theorem of
Erdos. The
last I heard (several years ago) it is an open problem for 'small' =
Lebesgue
measure zero.
***
Thanks, this is the kind of thing I was looking for, though it would be
nice to see one which was actually settled as true for category-small
but false for measure-small.
-- JS
________________________________________________________________________
Email and AIM finally together. You've gotta check out free AOL Mail! -
http://mail.aol.com
More information about the FOM
mailing list