A Primer of Lebesgue Integration
The Lebesgue 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. It is 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 powerful tools 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. Features: * The Riemann-Darboux Integral * The Riemann Integral as a Limit of Sums * Lebesgue Measure on (0.1) * Measurable-Sets - The Caratheodory Characterization
- Hardback | 184 pages
- 166.9 x 231.9 x 28.2mm | 716.68g
- 04 Apr 1995
- Elsevier Science Publishing Co Inc
- Academic Press Inc
- San Diego, United States
Prepublication Review "This is a wonderful little book that presents Lebesgue theory on the line and the plane as a completely natural extension of the familiar Reimann theory encountered in calculus...Ideal for a semester undergraduate course or seminar, though it is equally suitable for self-study...I especially recommend this book for students who plan to go on to graduate school in mathematics. If they didn't study it as an undergraduate, then it would be profitable reading for the summer before graduate school. With this background, the more general abstract theory of integration in graduate school will all seem natural...This book should do for real analysis what the famous old Knopp books have done for complex analysis. Of course, teachers of analysis will want copies on their shelves."
Table of contents
The Riemann-Darboux integral; the Riemann integral as a limit of sums; Lebesgue measure on (0,1); measurable sets - the caratheodory characterization; the Lebesgue integral for bounded functions; properties of the integral; the integral of unbounded functions; differentiation and integration; plane measure; the relationship between mu and lambda; general measures; integration for general measures; more integration; the Radon-Nikodym theorem; product measures; the space L2.