Skip to main content

Measure Extensions According to a Given Function

  • Conference paper
Optimization and Operations Research

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 157))

Abstract

The question how to make a real function measurable by an adequate extension1) of a given measure is motivated by problems of applied mathematics. The question arises especially in connection with the definition of any feasible “randomized extensions” of a game with non-denumerable many pure strategies.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. AUMANN, R.J.: Measurable utility and the measurable choice theorem. Proc.Coll.Intern. C.N.R.S. “La Décision”, Aixen-Provence, 15–26 (1967).

    Google Scholar 

  2. BIERLEIN, D.: Der Graph meßbarer Funktionen mit abstraktem Definitionsbereich. Math. Zeitschrift 76, 468–471 (1961).

    Article  Google Scholar 

  3. BIERLEIN, D.: Über die Fortsetzung von Wahrscheinlichkeits-feldern. Z.Wahrscheinlichkeitstheorie verw. Gebiete 1, 28–46 (1962).

    Article  Google Scholar 

  4. BIERLEIN, D.: Die Konstruktion eines Maßes … Z. Wahrscheinlichkeitstheorie verw. Gebiete 1, 126–140 (1962).

    Article  Google Scholar 

  5. HILDENBRAND, W.: Core and equilibria of a large economy. Princ. Univ. Press, Princeton,.

    Google Scholar 

  6. KURZ, A.: Uniformisierung analytischer Mengen und eine Anwendung bei der Maßfortsetzung. Archiv Math. 29, 204–207 (1977).

    Article  Google Scholar 

  7. LANDERS, D. and ROGGE, L.: On the extension problem for measures. Z. Wahrscheinlichkeitstheorie verw. Gebiete 30, 167–169 (1974).

    Article  Google Scholar 

  8. LEHN, J.: Maßfortsetzungen und Aumann’ s Selektionstheorem, Z. Wahrscheinlichkeitstheorie verw. Gebiete 35, 265–268 (1976).

    Article  Google Scholar 

  9. MARCZEWSKI, E.: Ensembles indépendants et … Fund.Math. 35, 13–28 (1968).

    Google Scholar 

  10. MERLO, J.C. and PANZONE, R.: Notes on the measure extension problem. Rev. Un. Mat. Argentina 23, 77–88 (1966/67).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1978 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bierlein, D. (1978). Measure Extensions According to a Given Function. In: Henn, R., Korte, B., Oettli, W. (eds) Optimization and Operations Research. Lecture Notes in Economics and Mathematical Systems, vol 157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-95322-4_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-95322-4_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08842-4

  • Online ISBN: 978-3-642-95322-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics