Abstract
The concept of “measure” (Sect. 6.1.2) is important for an understanding of the theory of the Lebesgue integral. A measure is a generalization of the concept of length that allows us to quantify the length of a set that is composed of, for instance, an infinite number of infinitesimal points with a highly discontinuous distribution. Thus, the Lebesgue integral is an effective tool for integrating highly discontinuous functions that cannot be integrated using conventional Riemann integrals.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Shima, H., Nakayama, T. (2009). Lebesgue Integrals. In: Higher Mathematics for Physics and Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/b138494_6
Download citation
DOI: https://doi.org/10.1007/b138494_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87863-6
Online ISBN: 978-3-540-87864-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)