(mathematical analysis, singular only, definite and countable) An integral which has more general application than that of the Riemann integral, because it allows the region of integration to be partitioned into not just intervals but any measurable sets for which the function to be integrated has a sufficiently narrow range. (Formal definitions can be found at PlanetMath).

plural of Lebesgue integral

(mathematical analysis) (of a set in some k-dimensional Euclidean space) That it is an element of the domain of the Lebesgue measure of the ambient Euclidean space.

(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).

plural of Lebesgue measure

(mathematics) A lemma, of importance in harmonic analysis and asymptotic analysis, stating that the Fourier transform or Laplace transform of an L1 function vanishes at infinity.