[FOM] Category and Measure
joeshipman at aol.com
Mon Sep 17 21:48:37 EDT 2007
From: Bill Taylor <W.Taylor at math.canterbury.ac.nz>
The two players alternately choose a closed sub-interval of the
interval. If the w-sequence of sub-intervals so obtained converges
to a point in some given BIG set, then B wins; otherwise A wins.
Mazur proved that if the target set was category-large, then B can
win (if he has first move). There is no similar result for measure.
Does "there is no similar result for measure" mean that there is a
target set whose complement is measure 0, which A, moving 2nd, can
always avoid? Or does it just mean that the question is open?
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