The first objective in Chapter 1 is to make plain what change is being made in the Riemann definition and to indicate why it should be beneficial. Then the definition of the generalized Riemann integral is formulated. It is given first for bounded intervals of real numbers and then, in the same language, for unbounded intervals. On the basis of these formulations the fundamental theorem of calculus linking integrals and derivatives is given an appealing form. Multiple integrals are defined, and again it is possible to use the same language as that first adopted for integration on a bounded real

EP - 46 ET - 1 PB - Mathematical Association of America PY - 1980 SN - 9780883850459 SP - 5 T2 - The Generalized Riemann Integral UR - http://www.jstor.org/stable/10.4169/j.ctt5hhb4z.6 VL - 20 Y2 - 2021/09/27/ ER -