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n-Dimensional Riemann-Stieltjes Integral

  • Richard M. Meyer
Part of the Universitext book series (UTX)

Abstract

We now generalize the results of Section 9 to consider the n-Dimensional (n > 1) Riemann-Stieltjes Integral with respect to an n-dimensional c.d.f., then, more generally, with respect to left-continuous n-dimensional b.v.f.’s. The development closely parallels that of the 1-dimensional case, and for this reason we will generally be briefer with proofs and descriptions than before. However, this by no means indicates that the n-dimensional Integral is any less important in applications.

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References to Additional and Related Material: Section 11

  1. 1.
    Bartle, R., “The Elements of Integration”, John Wiley and Sons, Inc. (1966).zbMATHGoogle Scholar
  2. 2.
    Gunther, N., “Sur les Integrales de Stieltjes”, Chelsea Publishing Company (1949).Google Scholar
  3. 3.
    Henstock, R., “Theory of Integration”, Butterworths (1963).Google Scholar
  4. 4.
    Hobson, E., “Theory of Functions of a Real Variable”, Vol. I, Dover Publications, Inc.Google Scholar
  5. 5.
    Kestelman, K., “Modern Theories of Integration”, Dover Publications, Inc.Google Scholar
  6. 6.
    Pesin, I., “Classical and Modern Integration Theories”, Academic Press (1970).Google Scholar
  7. 7.
    Zaanen, A., “An Introduction to the Theory of Integration”, North-Holland Publishing Co. (1958).Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • Richard M. Meyer
    • 1
  1. 1.Niagara University, College of Arts and SciencesNiagara UniversityUSA

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