1-Dimensional Riemann-Stieltjes Integral

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


Although the familiar Riemann Integral is sufficient for a wide variety of problem solving-purposes in Applied Mathematics, a generalization of it, known as the Riemann-Stieltjes Integral, must be called upon in many situations. In the present Section we shall develop what is termed a 1-dimensional Riemann-Stieltjes Integral, first with respect to a 1-dimensional c.d.f., then, more generally, with respect to b.v.f.


Continuous Function Bounded Interval Unbounded Interval Basic Definition Uniform Continuity 
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References to Additional and Related Material: Section 9

  1. 1.
    Bartle, R., “The Elements of Integration”, John Wiley and Sons, Inc. (1966).Google Scholar
  2. 2.
    Brand, L., “Advanced Calculus”, Wiley and Sons, Inc. (1958).Google Scholar
  3. 3.
    Cramer, H., “Mathematical Methods of Statistics”, Princeton University Press (1958).Google Scholar
  4. 4.
    Gunther, N., “Sur les Intégrales de Stieltjes”, Chelsea Publishing Company (1949).Google Scholar
  5. 5.
    Henstock, R., “Theory of Integration”, Butterworths (1963).Google Scholar
  6. 6.
    Hobson, E., “Theory of Functions of a Real Variable”, Vol. I, Dover Publications, Inc.Google Scholar
  7. 7.
    Kestelman, K., “Modern Theories of Integration”, Dover Publications, Inc.Google Scholar
  8. 8.
    Pesin, I., “Classical and Modern Integration Theories”, Academic Press (1970).Google Scholar
  9. 9.
    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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