Abstract
This chapter deals with the integration of essentially bounded measurable functions with respect to finitely additive measures like those that featured in the Yosida–Hewitt representation theorem in Chap. 3. The chapter includes a study of integration of an essentially bounded function u with respect to elements of, which leads to the multivalued essential range of u, and ends with an example of finitely additive measures that are not countably additive, but which coincide with Lebesgue measure when integrating continuous functions.
| Original language | English |
|---|---|
| Title of host publication | The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence |
| Place of Publication | Cham, Switzerland |
| Publisher | Springer Science and Business Media B.V. |
| Pages | 47-56 |
| Number of pages | 10 |
| ISBN (Electronic) | 9783030347321 |
| ISBN (Print) | 9783030347314 |
| DOIs | |
| Publication status | E-pub ahead of print - 3 Jan 2020 |
Publication series
| Name | SpringerBriefs in Mathematics |
|---|---|
| ISSN (Print) | 2191-8198 |
| ISSN (Electronic) | 2191-8201 |
Bibliographical note
Publisher Copyright:© 2020, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
ASJC Scopus subject areas
- General Mathematics