The Lebesgue measure is an extension of the classical notions of length and area to more complicated sets. Given an open set containing disjoint
intervals, the Lebesgue measure is defined by
Croft, H. T.; Falconer, K. J.; and Guy, R. K. Unsolved
Problems in Geometry. New York: Springer-Verlag, p. 4, 1991.Kestelman,
H. "Lebesgue Measure." Ch. 3 in Modern
Theories of Integration, 2nd rev. ed. New York: Dover, pp. 67-91, 1960.Ko,
K.-I. "A Polynomial-Time Computable Curve whose Interior has a Nonrecursive
Measure." Theoret. Comput. Sci.145, 241-270, 1995.