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