7. The Riemann–Stieltjes Integral

  1. Leonard F. Richardson

Published Online: 15 FEB 2011

DOI: 10.1002/9781118032411.ch7

Advanced Calculus: An Introduction to Linear Analysis

Advanced Calculus: An Introduction to Linear Analysis

How to Cite

Richardson, L. F. (2008) The Riemann–Stieltjes Integral, in Advanced Calculus: An Introduction to Linear Analysis, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118032411.ch7

  1. This chapter is not required for any subsequent chapters.

Publication History

  1. Published Online: 15 FEB 2011
  2. Published Print: 11 APR 2008

ISBN Information

Print ISBN: 9781118030677

Online ISBN: 9781118032411

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Keywords:

  • Riemann-Stieltjes integral;
  • bounded variation functions;
  • integrability theorems;
  • Riesz representation theorem;
  • integrals

Summary

This chapter contains sections titled:

  • Functions of Bounded Variation

  • Riemann-Stieltjes Sums and Integrals

  • Riemann-Stieltjes Integrability Theorems

  • The Riesz Representation Theorem

  • Test Yourself