 These partitions of formula_19 are subject to the outer measure.If for all possible such subsets formula_19 of the real numbers, the partitions of formula_19 cut apart by formula_6 have outer measures whose sum is the outer measure of formula_19, then the outer Lebesgue measure of formula_6 gives its Lebesgue measure.Intuitively, this condition means that the set formula_6 must not have some curious properties which causes a discrepancy in the measure of another set when formula_6 is used as a "mask" to "clip" that set, hinting at the existence of sets for which the Lebesgue outer measure does not give the Lebesgue measure.