MathDB
Miklos Schweitzer 1962_6

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September 18, 2008
real analysisreal analysis unsolved

Problem Statement

Let E E be a bounded subset of the real line, and let Ω \Omega be a system of (non degenerate) closed intervals such that for each x∈E x \in E there exists an I∈Ω I \in \Omega with left endpoint x x. Show that for every ε>0 \varepsilon > 0 there exists a finite number of pairwise non overlapping intervals belonging to Ω \Omega that cover E E with the exception of a subset of outer measure less than ε \varepsilon. [J. Czipszer]
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