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Mathematische Reihe

The Bochner Integral

Authors: Mikusinski, J.

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About this book

The theory of the Lebesgue integral is still considered as a difficult theory, no matter whether it is based the concept of measure or introduced by other methods. The primary aim of this book is to give an approach which would be as intelligible and lucid as possible. Our definition, produced in Chapter I, requires for its background only a little of the theory of absolutely convergent series so that it is understandable for students of the first undergraduate course. Nevertheless, it yields the Lebesgue integral in its full generality and, moreover, extends automatically to the Bochner integral (by replacing real coefficients of series by elements of a Banach space). It seems that our approach is simple enough as to eliminate the less useful Riemann integration theory from regular mathematics courses. Intuitively, the difference between various approaches to integration may be brought out by the following story on shoemakers. A piece of leather, like in Figure 1, is given. The task consists in measuring its area. There are three shoemakers and each of them solves the task in his own way. A B Fig. 1 The shoemaker R. divides the leather into a finite number of vertical strips and considers the strips approximately as rectangles. The sum of areas of all rectangles is taken for an approximate area of the leather (Figure 2). If he is not satisfied with the obtained exactitude, he repeats the whole procedure, by dividing the leather into thinner strips.

Table of contents (16 chapters)

Table of contents (16 chapters)

Buy this book

eBook 67,40 €
price for Spain (gross)
  • ISBN 978-3-0348-5567-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 83,19 €
price for Spain (gross)
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Bibliographic Information

Bibliographic Information
Book Title
The Bochner Integral
Authors
Series Title
Mathematische Reihe
Series Volume
55
Copyright
1978
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-5567-9
DOI
10.1007/978-3-0348-5567-9
Softcover ISBN
978-3-0348-5569-3
Edition Number
1
Number of Pages
XII, 233
Topics