In
mathematical analysis, a
measure on a
set is a systematic way to assign a number to each suitable
subset of that set, intuitively interpreted as its size. In this sense, a measure is a generalization of the concepts of length, area, and volume. A particularly important example is the
Lebesgue measure on a
Euclidean space, which assigns the conventional
length,
area, and
volume of
Euclidean geometry to suitable subsets of the -
dimensional Euclidean space . For instance, the Lebesgue measure of the
interval in the
real numbers is its length in the everyday sense of the word – specifically, 1.