Lebesgue measure [SEP] named after
Lebesgue measure
In measure theory, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of "n"-dimensional Euclidean space. For "n" = 1, 2, or 3, it coincides with the standard measure of length, area, or volume. In general, it is also called n"-dimensional volume, n"-volume, or simply volume. It is used throughout real analysis, in particular to define Lebesgue integration. Sets that can be assigned a Lebesgue measure are called
Luzin N property
In mathematics, a function "f" on the interval ["a", "b"] has the Luzin N property, named after Nikolai Luzin (also called Luzin property or N property) if for all formula_1 such that formula_2, there holds: formula_3, where formula_4 stands for the Lebesgue measure.
Note that the image of such a set "N" is not necessarily measurable, but since the Lebesgue measure is complete, it follows that if the Lebesgue outer measure of that set