Grundlehren der mathematischen Wissenschaften

Continuous Transformations in Analysis

With an Introduction to Algebraic Topology

Authors: Rado, Tibor, Reichelderfer, Paul V.

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About this book

The general objective of this treatise is to give a systematic presenta­ tion of some of the topological and measure-theoretical foundations of the theory of real-valued functions of several real variables, with particular emphasis upon a line of thought initiated by BANACH, GEOCZE, LEBESGUE, TONELLI, and VITALI. To indicate a basic feature in this line of thought, let us consider a real-valued continuous function I(u) of the single real variable tt. Such a function may be thought of as defining a continuous translormation T under which x = 1 (u) is the image of u. About thirty years ago, BANACH and VITALI observed that the fundamental concepts of bounded variation, absolute continuity, and derivative admit of fruitful geometrical descriptions in terms of the transformation T: x = 1 (u) associated with the function 1 (u). They further noticed that these geometrical descriptions remain meaningful for a continuous transformation T in Euclidean n-space Rff, where T is given by a system of equations of the form 1-/(1 ff) X-I U, . . . ,tt ,. ", and n is an arbitrary positive integer. Accordingly, these geometrical descriptions can be used to define, for continuous transformations in Euclidean n-space Rff, n-dimensional concepts 01 bounded variation and absolute continuity, and to introduce a generalized Jacobian without reference to partial derivatives. These ideas were further developed, generalized, and modified by many mathematicians, and significant applications were made in Calculus of Variations and related fields along the lines initiated by GEOCZE, LEBESGUE, and TONELLI.

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $109.00
price for USA in USD
  • ISBN 978-3-642-85989-2
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $139.99
price for USA in USD
  • ISBN 978-3-642-85991-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Continuous Transformations in Analysis
Book Subtitle
With an Introduction to Algebraic Topology
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
75
Copyright
1955
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag OHG. in Berlin, Göttingen and Heidelberg
eBook ISBN
978-3-642-85989-2
DOI
10.1007/978-3-642-85989-2
Softcover ISBN
978-3-642-85991-5
Series ISSN
0072-7830
Edition Number
1
Number of Pages
VIII, 442
Number of Illustrations
2 b/w illustrations
Topics