The book presents the development of the Lebesgue integral in such a way that usual approaches are explained. Namely, the Lebesgue integral can be built of a measure over a s-algebra (more generally, over any semiring, e.g. the intervals in the line or the bricks in Rn), or of a so-called Daniell-functional which is the would-be integral on some nice functions (the prime examples are the Riemann integral and its usual generalizations, in particular, the Riemann-Stieltjes integral in several variables). The author deems the second approach more powerful, but the other approach and their relation are also discussed in detail in Part I. Part II treats Fubini's theorem with special attention to the boundaries of its validity. Part III explains localizability and contains some stronger versions of the Radon-Nikodym theorem due to the author. Finally, complex measures are discussed. A useful Index completes the book. This volume is recommended to those who are familiar with calculus and are interested in the field of Lebesgue integral and the related theory of measures. It may be useful both for those first meeting the topic and for those deepening its understanding. So we propose it to students and researchers in mathematics, physics, engineering, etc.
"synopsis" may belong to another edition of this title.
Book Description Akademiai Kiado, 1998. Paperback. Book Condition: New. Bookseller Inventory # DADAX9630573466
Book Description Akademiai Kiado, 1998. Paperback. Book Condition: New. Ships with Tracking Number! INTERNATIONAL WORLDWIDE Shipping available. Buy with confidence, excellent customer service!. Bookseller Inventory # 9630573466n