Measure Theory

a branch of mathematics that studies the property of measures of sets. Measure theory developed on the basis of works by M. E. C. Jordan, E. Borel, and, particularly, H. Lebesgue at the end of the 19th century and the beginning of the 20th. In these works, the concepts of length, area, and volume were extended beyond the class of figures usually considered in geometry. As a consequence, measures in their most general meaning (completely additive set functions) became the subject of measure theory. The development of measure theory is closely related to the development of the theory of the integral.