Advertisement

Measure and Integration: Integral representations of isotone functionals

  • Heinz KönigEmail author
Chapter
  • 1.1k Downloads

Abstract

The present article is another continuation of the recent book of the author [1997] on measure and integration (cited as MI). The subsequent expository paper [1999] (cited as MI0) summarized the essentials, and went on to attain a standpoint which permits the competent evaluation of the traditional extension theories named after Daniell-Stone and Bourbaki, that is of those which start with certain isotone linear functionals. To this end the paper described without proof some further developments. The present article and its predecessor [1998] (cited as MI1) have the aim to elaborate these new developments in adequate contexts. While the previous one dealt with the measure-theoretic aspects proper as described in MI0 sections 1 and 4, the topic this time are certain isotone functionals and their integral representations. We shall elaborate the inner type development of MI sections 14 and 15 into parallel outer and inner representation theories, as formulated in MI0 section 3 as the decisive point for the purpose of that paper.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bassanezi, R.C. and G.H.Greco [1984] Sull’additività dell’integrale. Rend.Sem.Mat.Univ.Padova 72, 249-275.MathSciNetGoogle Scholar
  2. Bassanezi, R.C. and G.H.Greco [1988] On functionals representable by fuzzy measures. J.Math.Analysis Appl. 133, 44-56.MathSciNetCrossRefGoogle Scholar
  3. Choquet, G. [1953-54] Theory of capacities. Ann.Inst.Fourier (Grenoble) 5, 131-295.Google Scholar
  4. Greco, G.H. [1982] Sulla rappresentazione di funzionali mediante integrali.Rend.Sem.Mat.Univ.Padova 66, 21-42.MathSciNetzbMATHGoogle Scholar
  5. Köonig, H. [1997] Measure and Integration: An Advanced Course in Basic Procedures and Applications.Springer.Google Scholar
  6. Köonig, H. [1998] Measure and Integration: Mutual generation of outer and inner premeasures. These Annales 9, 99-122.MathSciNetzbMATHGoogle Scholar
  7. Köonig, H. [1999] Measure and integration: Comparison of old and new procedures.Arch.Math. 72, 192-205.MathSciNetCrossRefGoogle Scholar
  8. Nguyen, H.T. and E.A.Walker [1997] A First Course in Fuzzy Logic.CRC Press.Google Scholar

Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Fachbereich MathematikUniversität des SaarlandesSaarbrückenGermany

Personalised recommendations