TY - CHAP
T1 - Integration and Finitely Additive Measures
AU - Toland, John
N1 - Publisher Copyright:
© 2020, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2020/1/3
Y1 - 2020/1/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85101147237&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-34732-1_6
DO - 10.1007/978-3-030-34732-1_6
M3 - Chapter or section
AN - SCOPUS:85101147237
SN - 9783030347314
T3 - SpringerBriefs in Mathematics
SP - 47
EP - 56
BT - The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence
PB - Springer Science and Business Media B.V.
CY - Cham, Switzerland
ER -