Measure, Integral, Derivative [electronic resource] :A Course on Lebesgue's Theory / by Sergei Ovchinnikov.
by Ovchinnikov, Sergei [author.]; SpringerLink (Online service).
Material type:
Item type | Current location | Call number | Status | Date due | Barcode |
---|---|---|---|---|---|
MAIN LIBRARY | QA312-312.5 (Browse shelf) | Available |
Browsing MAIN LIBRARY Shelves Close shelf browser
BF81-107.L4 Film, Television and the Psychology of the Social Dream | QH359-425 Primates, Pathogens, and Evolution | R895-920 Dermatologic Ultrasound with Clinical and Histologic Correlations | QA312-312.5 Measure, Integral, Derivative | QK900-989 Invasion of Woody Legumes | R895-920 Atlas of Gynecologic Oncology Imaging | RC952-954.6 Exercise and Physical Functioning in Osteoarthritis |
1 Preliminaries -- 2 Lebesgue Measure -- 3 Lebesgue Integration -- 4 Differentiation and Integration -- A Measure and Integral over Unbounded Sets -- Index.
This classroom-tested text is intended for a one-semester course in Lebesgue’s theory. With over 180 exercises, the text takes an elementary approach, making it easily accessible to both upper-undergraduate- and lower-graduate-level students. The three main topics presented are measure, integration, and differentiation, and the only prerequisite is a course in elementary real analysis. In order to keep the book self-contained, an introductory chapter is included with the intent to fill the gap between what the student may have learned before and what is required to fully understand the consequent text. Proofs of difficult results, such as the differentiability property of functions of bounded variations, are dissected into small steps in order to be accessible to students. With the exception of a few simple statements, all results are proven in the text. The presentation is elementary, where σ-algebras are not used in the text on measure theory and Dini’s derivatives are not used in the chapter on differentiation. However, all the main results of Lebesgue’s theory are found in the book.
There are no comments for this item.