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- W1575995836 abstract "We prove theorems of the following form: if $Asubseteq {mathbb R}^2$ is a big set, then there exists a big set $Psubseteq {mathbb R}$ and a perfect set $Qsubseteq {mathbb R}$ such that $Ptimes Qsubseteq A$. We discuss cases where big set means: set of positive Lebesgue measure, set of full Lebesgue measure, Baire measurable set of second Baire category and comeagre set. In the first case (set of positive measure) we obtain the theorem due to Eggleston. In fact we give a simplified version of the proof given by J. Cichon. To prove these theorems we use Shoenfield's theorem about absoluteness for $Sigma^1_2$-sentences." @default.
- W1575995836 created "2016-06-24" @default.
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- W1575995836 date "2002-04-10" @default.
- W1575995836 modified "2023-09-27" @default.
- W1575995836 title "Nonstandard proofs of Eggleston like theorems" @default.
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