 The total length of any covering interval set can easily overestimate the measure of formula_6, because formula_6 is a subset of the union of the intervals, and so the intervals may include points which are not in formula_6.The Lebesgue outer measure emerges as the greatest lower bound (infimum) of the lengths from among all possible such sets.Intuitively, it is the total length of those interval sets which fit formula_6 most tightly and do not overlap.