Integral of Real-Valued Functions

Carlos S. Kubrusly
Additional contact information
Carlos S. Kubrusly: Catholic University of Rio de Janeiro, Electrical Engineering Department

Chapter 4 in Essentials of Measure Theory, 2015, pp 57-69 from Springer

Abstract: Abstract A real-valued function $$f: X\! \rightarrow \mathbb{R}$$ on X can be expressed as $$f = f^{+} - f^{-}\!$$ , where the nonnegative functions $$f^{+}: X\! \rightarrow \mathbb{R}$$ and $$f^{-}: X\! \rightarrow \mathbb{R}$$ are the positive and negative parts of f. If f is measurable, then so are f + and f − (Proposition 1.6). Integration of measurable real-valued functions, leading to real-valued integrals, are considered by using the above decomposition.

Keywords: Convergence Theorem; Measure Space; Dominate Convergence Theorem; Monotone Convergence Theorem; Riemann Integrable (search for similar items in EconPapers)
Date: 2015
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-22506-7_4

Ordering information: This item can be ordered from
http://www.springer.com/9783319225067

DOI: 10.1007/978-3-319-22506-7_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().