The Lebesgue Integral
The Lebesgue Integral
$60.00
USDUsing the Daniell–Riesz approach, this text presents the Lebesgue integral at a level accessible to an audience familiar only with limits, derivatives and series. Employing such minimal prerequisites allows for greatly increased curricular flexibility for course instructors, as well as providing undergraduates with a gateway to the powerful modern mathematics of functions at a very early stage. The book's topics include: the definition and properties of the Lebesgue integral; Banach and Hilbert spaces; integration with respect to Borel measures, along with their associated L2(μ) spaces; bounded linear operators; and the spectral theorem. The text also describes several applications of the theory, such as Fourier series, quantum mechanics, and probability.
- Introduces readers to the powerful theory of Lebesgue integration with fewer prerequisites than many other approaches
- As a textbook, it allows for increased flexibility in the undergraduate analysis syllabus
- Describes several applications, such as Fourier series, quantum mechanics, and probability
Product details
September 2015Hardback
9781939512079
295 pages
260 × 182 × 20 mm
0.65kg
This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
Table of Contents
- Preface
- Introduction
- 1. Lebesgue integrable functions
- 2. Lebesgue's integral compared to Riemann's
- 3. Functions spaces
- 4. Measure theory
- 5. Hilbert space operators
- Solutions to selected problems
- Bibliography.
