A word in response to the corona virus crisis: Your print orders will be fulfilled, even in these challenging times. If you don’t want to wait – have a look at our ebook offers and start reading immediately.

SpringerBriefs in Mathematics

The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence

A Primer

Authors: Toland, John

Free Preview

Buy this book

eBook 42,79 €
price for Spain (gross)
  • ISBN 978-3-030-34732-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-3-030-34731-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

In measure theory, a familiar representation theorem due to F. Riesz identifies the dual space Lp(X,L,λ)* with Lq(X,L,λ), where 1/p+1/q=1, as long as 1 ≤ p<∞. However, L(X,L,λ)* cannot be similarly described, and is instead represented as a class of finitely additive measures.

This book provides a reasonably elementary account of the representation theory of L(X,L,λ)*, examining pathologies and paradoxes, and uncovering some surprising consequences. For instance, a necessary and sufficient condition for a bounded sequence in L(X,L,λ) to be weakly convergent, applicable in the one-point compactification of X, is given.

With a clear summary of prerequisites, and illustrated by examples including L(Rn) and the sequence space l, this book makes possibly unfamiliar material, some of which may be new, accessible to students and researchers in the mathematical sciences.

About the authors

John Toland FRS is a mathematical analyst who worked in nonlinear partial differential equations and served as Director of the Isaac Newton Institute for Mathematical Sciences in Cambridge (2011-2016). He was awarded the London Mathematical Society Berwick Prize (2000) and the Royal Society Sylvester Medal (2012).

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook 42,79 €
price for Spain (gross)
  • ISBN 978-3-030-34732-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-3-030-34731-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence
Book Subtitle
A Primer
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-34732-1
DOI
10.1007/978-3-030-34732-1
Softcover ISBN
978-3-030-34731-4
Series ISSN
2191-8198
Edition Number
1
Number of Pages
X, 99
Number of Illustrations
1 b/w illustrations
Topics