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
Lebesgue measurable; the measure of the Lebesgue measurable set
A is denoted by λ(
A).