A non-standard integration theory for unbounded functions

  • Allen R. Bernstein
  • Peter A. Loeb
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 369)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. BERNSTEIN, Invariant subspaces for linear operators, doctoral dissertation, U.C.L.A. 1965, unpublished.Google Scholar
  2. [2]
    —, Invariant subspaces of polynomially compact operators on Banach space, Pac. J. of Math., 21(1967), pp. 445–463.MathSciNetCrossRefGoogle Scholar
  3. [3]
    —, A non-standard integration theory for unbounded functions, University of Maryland Technical Report, TR 71-50, 1971.Google Scholar
  4. [4]
    —, Invariant subspaces for certain commuting operators on Hilbert space, Annals of Math., 95(1972), pp. 253–260.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    A. BERNSTEIN and A. ROBINSON, Solution of an invariant subspace problem of K. T. Smith and P. R. Halmos, Pac. J. of Math., 16(1966), pp. 421–431.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    A. BERNSTEIN and F. WATTENBERG, Non-Standard Measure Theory, Applications of Model Theory to Algebra, Analysis and Probability, ed. W. A. J. Luxemburg, Holt, Rinehart and Winston, 1969.Google Scholar
  7. [7]
    C. HENSON, On the non-standard representation of measures, Trans. Amer. Math. Soc., 172, October, 1972, pp. 437–446.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    P. A. LOEB, A non-standard representation of measurable spaces and L, Bull. Amer. Math. Soc., 77, No. 4, July 1971, pp. 540–544.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    —, A non-standard representation of measurable spaces, L and L*, Contributions to Non-Standard Analysis, Ed. by W. A. J. Lexemburg and A. Robinson, North-Holland, 1972, pp. 65–80.Google Scholar
  10. [10]
    —, A non-standard representation of Borel measures and σ-finite measures, this volume.Google Scholar
  11. [11]
    A. ROBINSON, Non-Standard Analysis, North Holland, Amsterdam, 1966.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • Allen R. Bernstein
    • 1
  • Peter A. Loeb
    • 2
  1. 1.University of MarylandUSA
  2. 2.Yale University and University of IllinoisUrbana

Personalised recommendations