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Mathematics and Its Applications

Nonstandard Analysis and Vector Lattices

Editors: Kutateladze, Semën Samsonovich (Ed.)

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About this book

Nonstandard methods of analysis consist generally in comparative study of two interpretations of a mathematical claim or construction given as a formal symbolic expression by means of two different set-theoretic models: one, a "standard" model and the other, a "nonstandard" model. The second half of the twentieth century is a period of significant progress in these methods and their rapid development in a few directions. The first of the latter appears often under the name coined by its inventor, A. Robinson. This memorable but slightly presumptuous and defiant term, non­ standard analysis, often swaps places with the term Robinsonian or classical non­ standard analysis. The characteristic feature of Robinsonian analysis is a frequent usage of many controversial concepts appealing to the actual infinitely small and infinitely large quantities that have resided happily in natural sciences from ancient times but were strictly forbidden in modern mathematics for many decades. The present-day achievements revive the forgotten term infinitesimal analysis which reminds us expressively of the heroic bygones of Calculus. Infinitesimal analysis expands rapidly, bringing about radical reconsideration of the general conceptual system of mathematics. The principal reasons for this progress are twofold. Firstly, infinitesimal analysis provides us with a novel under­ standing for the method of indivisibles rooted deeply in the mathematical classics.

Table of contents (5 chapters)

  • Nonstandard Methods and Kantorovich Spaces

    Kusraev, A. G. (et al.)

    Pages 1-79

  • Functional Representation of a Boolean Valued Universe

    Gutman, A. E. (et al.)

    Pages 81-104

  • Dual Banach Bundles

    Gutman, A. E. (et al.)

    Pages 105-159

  • Infinitesimals in Vector Lattices

    Emel’yanov, È. Yu.

    Pages 161-230

  • Vector Measures and Dominated Mappings

    Kusraev, A. G. (et al.)

    Pages 231-299

Buy this book

eBook $99.00
price for USA in USD (gross)
  • ISBN 978-94-011-4305-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $129.00
price for USA in USD
  • ISBN 978-94-010-5863-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Nonstandard Analysis and Vector Lattices
Editors
  • Semën Samsonovich Kutateladze
Series Title
Mathematics and Its Applications
Series Volume
525
Copyright
2000
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-011-4305-9
DOI
10.1007/978-94-011-4305-9
Softcover ISBN
978-94-010-5863-6
Edition Number
1
Number of Pages
XII, 307
Topics