Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-27T19:13:34.561Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE POSITIVITY OF RIEMANN–STIELTJES INTEGRALS

Part of: Real functions

Published online by Cambridge University Press:  02 August 2012

JANI LUKKARINEN  and
MIKKO S. PAKKANEN
JANI LUKKARINEN
Affiliation:
Department of Mathematics and Statistics, University of Helsinki, PO Box 68, FI-00014 Helsingin yliopisto, Finland (email: [email protected])
MIKKO S. PAKKANEN*
Affiliation:
CREATES and Department of Economics and Business, Aarhus University, Bartholins Allé 10, DK-8000 Aarhus C, Denmark (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study the question whether a Riemann–Stieltjes integral of a positive continuous function with respect to a nonnegative function of bounded variation is positive.

Keywords

Riemann–Stieltjes integralpositivityfunction of bounded variationGrönwall’s inequality

MSC classification

Secondary: 26A42: Integrals of Riemann, Stieltjes and Lebesgue type
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 3 , June 2013 , pp. 400 - 405
Copyright
Copyright © 2012 Australian Mathematical Publishing Association Inc. 

References

[1]Beesack, P. R., ‘Bounds for Riemann–Stieltjes integrals’, Rocky Mountain J. Math. 5 (1975), 75–78.CrossRefGoogle Scholar
[2]Ethier, S. N. & Kurtz, T. G., Markov Processes: Characterization and Convergence (Wiley, New York, 1986).CrossRefGoogle Scholar
[3]Ganelius, T., ‘Un théorème taubérien pour la transformation de Laplace’, C. R. Acad. Sci. Paris 242 (1956), 719–721.Google Scholar
[4]Hewitt, E. & Stromberg, K., Real and Abstract Analysis (Springer, New York, 1965).Google Scholar
[5]Hildebrandt, T. H., Introduction to the Theory of Integration (Academic Press, New York, 1963).Google Scholar
[6]Knowles, I., ‘Integral mean value theorems and the Ganelius inequality’, Proc. Roy. Soc. Edinburgh Sect. A 97 (1984), 145–150.CrossRefGoogle Scholar
[7]Protter, M. H. & Morrey, C. B., A First Course in Real Analysis (Springer, New York, 1977).CrossRefGoogle Scholar
[8]Rudin, W., Principles of Mathematical Analysis (McGraw-Hill, New York, 1953).Google Scholar
[9]Satyanarayana, U. V., ‘A note on Riemann–Stieltjes integrals’, Amer. Math. Monthly 87 (1980), 477–478.CrossRefGoogle Scholar