MathDB
Miklos Schweitzer 1976_6

Source: Measure Theory

December 30, 2008
real analysisreal analysis unsolved

Problem Statement

Let 0≤c≤1 0 \leq c \leq 1, and let η \eta denote the order type of the set of rational numbers. Assume that with every rational number r r we associate a Lebesgue-measurable subset Hr H_r of measure c c of the interval [0,1] [0,1]. Prove the existence of a Lebesgue-measurable set H⊂[0,1] H \subset [0,1] of measure c c such that for every x∈H x \in H the set {r:  x∈Hr } \{r : \;x \in H_r\ \} contains a subset of type η \eta. M. Laczkovich
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