Riemann integral.

Description
Riemann conditions and Riemann theorem for double integral are stated. Some more theorems on integral are stated and proved. Fubini theorem for double integral is stated and proved. Integration as an area is explained. The geometrical interpretation of integral is discussed here. Properties of double integral such as Linearity, comparision and additivity etc. are discussed. The criterion that a bounded set in a plane is to be Jordarn- measurable are discussed in this lecture note.
Prof. James McKernan, Maths, 18.024. Calculus with Theory II, Spring 2003: Notes on double integrals: Massachusetts Institute of Technology: MIT OpenCourseWare),http://ocw.mit.edu (Accessed October 21, 2011). License: Creative Commons BY-NC-SA:http://ocw.mit.edu/terms/#cc