‘A Concise Introduction to the Theory of Integration’ was once a best-sellingBirkhäuser title which published 3 editions. This manuscript is a substantialrevision of the material. Chapter one now includes a section about the rate of convergence of Riemann sums. The second chapter now covers both Lebesgue andBernoulli measures, whose relation to one another is discussed. The third chapter now includes a proof of Lebesgue's differential theorem for all monotone functions. This is a beautiful topic which is not often covered. The treatmentof surface measure and the divergence theorem in the fifth chapter has been improved. Loose ends from the discussion of the Euler-MacLauren in Chapter I are tied together in Chapter seven. Chapter eight has been expanded to include aproof of Carathéory's method for constructing measures; his result is appliedto the construction of Hausdorff measures. The new material is complemented by the addition of several new problems based on that material. Refocus and substantial revision of previous successful publication 'A Concise Introduction to the Theory of Integration' by D.W. Stroock (Birkhauser). Separate solutions manual available to those who adopt the textbook. New material is complementedby the addition of several new problems. INDICE: -Preface.-1. The Classical Theory.-2. Measures. -3. Lebesgue Integration.-4. Products of Measures.-5. Changes of Variable.-6. Basic Inequalitiesand Lebesgue Spaces.-7. Hilbert Space and Elements of Fourier Analysis.-8. The Radon-Nikodym Theorem, Daniell
- ISBN: 978-1-4614-1134-5
- Editorial: Springer New York
- Encuadernacion: Cartoné
- Páginas: 244
- Fecha Publicación: 28/09/2011
- Nº Volúmenes: 1
- Idioma: Inglés