logo
Supporting your high street Find out how »
Basket Image

Basket

Real Analysis, PDF eBook
Please note: eBooks can only be purchased with a UK issued credit card and all our eBooks (ePub and PDF) are DRM protected.

Description

This book is a self-contained introduction to real analysis assuming only basic notions on limits of sequences in ]RN, manipulations of series, their convergence criteria, advanced differential calculus, and basic algebra of sets.

The passage from the setting in ]RN to abstract spaces and their topologies is gradual.

Continuous reference is made to the ]RN setting, where most of the basic concepts originated.

The first seven chapters contain material forming the backbone of a basic training in real analysis.

The remaining two chapters are more topical, relating to maximal functions, functions of bounded mean oscillation, rearrangements, potential theory, and the theory of Sobolev functions.

Even though the layout of the book is theoretical, the entire book and the last chapters in particular concern applications of mathematical analysis to models of physical phenomena through partial differential equations.

The preliminaries contain a review of the notions of countable sets and related examples.

We introduce some special sets, such as the Cantor set and its variants, and examine their structure.

These sets will be a reference point for a number of examples and counterexamples in measure theory (Chapter II) and in the Lebesgue differentiability theory of absolute continuous functions (Chapter IV).

This initial chapter also contains a brief collection of the various notions of ordering, the Hausdorff maximal principle, Zorn's lemma, the well-ordering principle, and their fundamental connections.

Information

Other Formats

£64.99

£55.24

Available to Download
 
Delivered to your inbox

to transfer to your device

Also by Emmanuele DiBenedetto   |  View all

Also in the Birkhauser Advanced Texts Basler Lehrbucher series   |  View all