 It follows that for any point "x" in "E",

Hence, by the Loomis–Whitney inequality,

and hence

The quantity

can be thought of as the average width of formula_18 in the formula_19th coordinate direction.This interpretation of the Loomis–Whitney inequality also holds if we consider a finite subset of Euclidean space and replace Lebesgue measure by counting measure.The Loomis–Whitney inequality is a special case of the Brascamp–Lieb inequality, in which the projections "πj" above are replaced by more general linear maps, not necessarily all mapping onto spaces of the same dimension.