Integration is one of the two cornerstones of analysis. In the fundamental work of Lebesgue, integration is presented in terms of measure theory. This introductory text starts with the historical development of the notion of set theory and integral theory. From here, the reader is naturally led to the consideration of the Lebesgue Integral, where abstract integration is developed via the measure theory. The important topics like the Outer Measure, Cantor's Ternary Set, Measurable Function, the Lebesgue Integral, Fundamental Theorem of Calculus, Lp-spaces, Fubini's Theorem, the Radon-Nikodym Theorem, and so on are discussed. The text is written in an informal style to make the subject matter easily comprehensible. Concepts have been developed with the help of motivating examples and probing questions, followed by numerous exercises. The book is suitable both as a textbook for an introductory course on the topic or for self-study. The core material is interspersed with examples, theorems, recapitulations, multiple choice questions, true/false questions and fill-in-the-blanks questions after relevant discussions of the topics.
- ISBN13 9789385909436
- Publish Date 30 September 2017
- Publish Status Active
- Publish Country IN
- Imprint I K International Publishing House Pvt. Ltd
- Format Paperback
- Pages 176
- Language English