## Lebesgue Measure

An extension of the classical notions of length and Area to more complicated sets. Given an open set containing Disjoint intervals,

Given a Closed Set ,

A unit Line Segment has Lebesgue measure 1; the Cantor Set has Lebesgue measure 0. The Minkowski Measure of a bounded, Closed Set is the same as its Lebesgue measure (Ko 1995).

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.