ABSTRACT
The concepts of length, area, volume, mass, and weight are familiar in measuring the sizes of various geometrical objects, and are usually treated in the study of elementary calculus. Typically these are nonnegative values attached to certain elementary figures such as intervals, rectangles, spheres, or balls. In this chapter, the authors introduce the Riemann-Darboux sums and the consequent integral. More complicated structures appear in real problems. They must be measured and suitable numerical values assigned. This leads to analyses of objects which are composed of (or obtained from) elementary figures in the sense of using sums (or unions), differences (or intersections), and other decompositions. The chapter discusses space R model with proofs. It also includes multiple exercises that help students try themselves and measure theory and integration.
