Noun
Lebesgue measure (plural Lebesgue measures)
(mathematical analysis) A unique complete translation-invariant measure for the σ-algebra which contains all k-cells in a given Euclidean space, and which assigns a measure to each k-cell which is equal to that k-cell's volume (as defined in Euclidean geometry: i.e., the volume of the k-cell equals the product of the lengths of its sides).
Along with the above remarks about measure, it shows that the set of Liouville numbers and its complement decompose the reals into two sets, one of which is meagre, and the other of Lebesgue measure zero. Source: Internet
An example of this is the Smith–Volterra–Cantor set which has topological dimension 0 yet has positive 1-dimensional Lebesgue measure. Source: Internet
For example, the real numbers with the standard Lebesgue measure are σ-finite but not finite. Source: Internet
In Lebesgue measure theory, the Cantor set is an example of a set which is uncountable and has zero measure. Source: Internet
However, the seminorm is equal to zero for any function supported on a set of Lebesgue measure zero. Source: Internet
Mandler accepts that, under either model of production, the initial endowments will not be consistent with a continuum of equilibria, except for a set of Lebesgue measure zero. Source: Internet