AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIA-PAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.-CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN
|
|||||||
The STUDIA UNIVERSITATIS BABEŞ-BOLYAI issue article summary The summary of the selected article appears at the bottom of the page. In order to get back to the contents of the issue this article belongs to you have to access the link from the title. In order to see all the articles of the archive which have as author/co-author one of the authors mentioned below, you have to access the link from the author's name. |
|||||||
STUDIA MATHEMATICA - Issue no. 4 / 2010 | |||||||
Article: |
BOOK REVIEWS: JOHN J. BENEDETTO AND WOJCIECH CZAJA, INTEGRATION AND MODERN ANALYSIS, XIX+575 PP,BIRKHÄUSER ADVANCED TEXTS, BIRKHÄUSER, BOSTON -BASEL - BERLIN, 2009, ISBN: 978-0-8176-4306-5, E-ISBN: 978-0-8176-4656-1. Authors: ŞTEFAN COBZAŞ. |
||||||
Abstract: The aim of the present book is to emphasize how the modern integration theory evolved from some classical problems in function theory, related mainly to Fourier analysis. It is worth to mention that some problems that arose in the study of Fourier series in the nineteenth century lay at the basis of many modern branches of mathematics as, for instance, set theory. For this reason the first chapter of the book, Ch. 1, Classical real variables, contains some classical results related to differentiation (e.g., continuous nowhere differentiable functions) and its imperfect relations with the Riemann integral, culminating in the new theory of integration developed by Lebesgue, which put the things in their right places. In fact, one of the main ideas of the book is the study of the relations between integrals and the a.e. derivatives (the Fundamental Theorem of Calculus - FTC), realized by the key notion of absolute continuity, viewed by the authors as a unifying concept for the FTC, Lebesgue dominated convergence theorem (LDC) and Radon-Nikodym theorem. | |||||||