Abstract
In this chapter we discuss a generalization of the Riemann integral that is often used in both theoretical and applied mathematics. Stieltjes originally introduced this concept to deal with infinite continued fractions, but it was soon apparent that the concept is useful in other areas of mathematics—and thus in mathematical physics, probability, and number theory, independently of its role in continued fractions. We illustrate the usefulness of the concept with two simple examples.
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- 1.
Thomas Joannes Stieltjes (1856–1894), Dutch mathematician.
- 2.
For more on continued fractions, see [5].
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Laczkovich, M., Sós, V.T. (2015). The Stieltjes Integral. In: Real Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2766-1_18
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DOI: https://doi.org/10.1007/978-1-4939-2766-1_18
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-2765-4
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