The Lebesgue-Stieltjes integral: a practical introduction
The Lebesgue-Stieltjes integral: a practical introduction By Carter M., van Brunt B.
2000 | 241 Pages | ISBN: 0387950125 | DJVU | 2 MB
2000 | 241 Pages | ISBN: 0387950125 | DJVU | 2 MB
"The authors aim to introduce the Lebesgue-Stieltjes integral on the real line in a natural way as an extension of the Riemann integral. They made the treatment as practical as possible. The evaluation of Lebesgue-Stieltjes integrals is discussed in detail, as are the key theorems of integral calculus as well as the standard convergence theorems. The book then concludes with a brief discussion of multivariate integrals and surveys of L[superscript p] spaces and some applications. Exercises, which extend and illustrate the theory, and provide practice in techniques, are included."--BOOK JACKET. 1. Real Numbers -- 2. Some Analytic Preliminaries -- 3. The Riemann Integral -- 4. The Lebesgue-Stieltjes Integral -- 5. Properties of the Integral -- 6. Integral Calculus -- 7. Double and Repeated Integrals -- 8. The Lebesgue Spaces L[superscript p] -- 9. Hilbert Spaces and L[superscript 2] -- 10. Epilogue -- Appendix: Hints and Answers to Selected Exercises