'A Concise Introduction to the Theory of Integration' was once a best-selling Birkhauser title which published 3 editions. This manuscript is a substantial revision of the material. Chapter one now includes a section about the rate of convergence of Riemann sums. The second chapter now covers both Lebesgue and Bernoulli 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 treatment of 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 a proof of Caratheory's method for constructing measures; his result is applied to the construction of Hausdorff measures. The new material is complemented by the addition of several new problems based on that material.
- ISBN10 146141136X
- ISBN13 9781461411369
- Publish Date 2 August 2011
- Publish Status Withdrawn
- Out of Print 18 October 2014
- Publish Country US
- Imprint Springer
- Format Paperback (US Trade)
- Pages 256
- Language English