The Lebesgue integral is the standard tool for mathematics, physics, or engineering. It is used where sequences or series arise and where one might wish to express the integral of a sum of integrals or vice versa. Itis essential in Fourier analysis and for the construction of Hilbert space and other function spaces. This primer gives a concrete treatment, building Lebesgue theory in a way parallel to the Riemann integral of beginning calculus. It makes the powerfultools of Lebesgue theory readily available to those in applied areas. It is a good introduction for those going on in mathematics as well as a refresher holding new insights for those in the field.
Professor Bear gives a clear and engaging account of this important and previously forbidding piece of mathematics, providing readers with a key to many areas of analysis.
*
* The Riemann-Darboux Integral
* The Riemann Integral as a Limit of Sums
* Lebesgue Measure on (0.1)
* Measurable-Sets - The Caratheodory Characterization
H.S. Bear is a professor at the University of Hawaii, Manoa and a member of both the American Mathematical Society and the Mathematical Association of America.