Schmidt's Game and Vitali Sets
Abstract
While many types of non-measurable sets are never (α, β)-winning in the sense of Schmidt's game, we show that this is not the case for certain Vitali sets. Our main theorems show that for certain values of α, β one can construct a Vitali set which is (α, β)-winning, while for other values of α,β every Vitali set is (α,β)-losing. We also investigate the (α,β)-Schmidt game for various other types of pathological sets, highlighting their differences from Vitali sets.
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