Mathematische Reihe

# The Bochner Integral

Authors: Mikusinski, J.

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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.

• The Lebesgue Integral

Pages 1-7

Mikusiński, Jan

• Banach Space

Pages 8-14

Mikusiński, Jan

• The Bochner Integral

Pages 15-22

Mikusiński, Jan

• Axiomatic Theory of the Integral

Pages 23-36

Mikusiński, Jan

• Applications to Set Theory

Pages 37-39

Mikusiński, Jan

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
Softcover 83,19 €
price for Spain (gross)
• ISBN 978-3-0348-5569-3
• 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
• The final prices may differ from the prices shown due to specifics of VAT rules

## Bibliographic Information

Bibliographic Information
Book Title
The Bochner Integral
Authors
Series Title
Mathematische Reihe
Series Volume
55
1978
Publisher
Birkhäuser Basel