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- W4294410636 abstract "The main goal of this note is to prove the following theorem. If $A_n$ is a sequence of measurable sets in a $sigma$-finite measure space $(X, mathcal{A}, mu)$ that covers $mu$-a.e. $x in X$ infinitely many times, then there exists a sequence of integers $n_i$ of density zero so that $A_{n_i}$ still covers $mu$-a.e. $x in X$ infinitely many times. The proof is a probabilistic construction. As an application we give a simple direct proof of the known theorem that the ideal of density zero subsets of the natural numbers is random-indestructible, that is, random forcing does not add a co-infinite set of naturals that almost contains every ground model density zero set. This answers a question of B. Farkas." @default.
- W4294410636 created "2022-09-03" @default.
- W4294410636 creator A5068411412 @default.
- W4294410636 date "2011-09-22" @default.
- W4294410636 modified "2023-09-30" @default.
- W4294410636 title "A covering theorem and the random-indestructibility of the density zero ideal" @default.
- W4294410636 doi "https://doi.org/10.48550/arxiv.1109.4858" @default.
- W4294410636 hasPublicationYear "2011" @default.
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