Skip to main content

A nonstandard representation of Borel measures and σ-finite measures

Part of the Lecture Notes in Mathematics book series (LNM,volume 369)

Keywords

  • Borel Measure
  • Infinite Element
  • Finite Borel Measure
  • Positive Natural Number
  • Nonstandard Representation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bernstein, A.R., and Wattenberg, F., Nonstandard Measure Theory, Applications of Model Theory to Algebra, Analysis, and Probability, Edited by W. A. J. Luxemburg, pp. 171–185, Holt, Rinehart and Winston, 1969.

    Google Scholar 

  2. Henson, C. W., On the Nonstandard Representation of Measures, Trans. Amer. Math. Soc. 172, Oct. 1972, pp. 437–446.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Loeb, P. A., A Nonstandard Representation of Measurable Spaces and L, Bull. Amer. Math. Soc. 77, No. 4, July 1971, pp. 540–544.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. ____, A Nonstandard Representation of Measurable Spaces L and L * , Contributions to Non-Standard Analysis, Edited by W. A. J. Luxemburg and A. Robinson, North-Holland, 1972, pp. 65–80.

    Google Scholar 

  5. Robertson, A. P., and Kingman, J. F. C., On a Theorem of Lyapunov, The Journal of the London Mathematical Society, Vol. 43, 1968, pp. 347–351.

    MathSciNet  MATH  Google Scholar 

  6. Robinson, A., On Generalized Limits and Linear Functions, Pacific J. Math, 14, 1964, pp. 269–283.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Robinson, A., Non-Standard Analysis, North-Holland, 1966.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1974 Springer-Verlag

About this paper

Cite this paper

Loeb, P.A. (1974). A nonstandard representation of Borel measures and σ-finite measures. In: Hurd, A., Loeb, P. (eds) Victoria Symposium on Nonstandard Analysis. Lecture Notes in Mathematics, vol 369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066008

Download citation

  • DOI: https://doi.org/10.1007/BFb0066008

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06656-9

  • Online ISBN: 978-3-540-37928-7

  • eBook Packages: Springer Book Archive