[FOM] Category and Measure

Bill Taylor W.Taylor at math.canterbury.ac.nz
Mon Sep 17 20:38:37 EDT 2007

This isn't really a result in analysis, as asked for, but could be
regarded as an "application", to game theory.   Namely, Mazur's game.

The two players alternately choose a closed sub-interval of the previous
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.

Bill Taylor

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