TY - CHAP
T1 - 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 introduces basic notation and definitions, for example, of partial ordering, lattice operations, absolute continuity and singularity, for finitely additive measures. The important notion of pure finite additivity of measures follows, and it is shown that every finitely additive measure is uniquely the sum of a countably additive and a purely finitely additive measure. This sets the scene for the material that follows.
AB - This chapter introduces basic notation and definitions, for example, of partial ordering, lattice operations, absolute continuity and singularity, for finitely additive measures. The important notion of pure finite additivity of measures follows, and it is shown that every finitely additive measure is uniquely the sum of a countably additive and a purely finitely additive measure. This sets the scene for the material that follows.
UR - http://www.scopus.com/inward/record.url?scp=85101151117&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-34732-1_4
DO - 10.1007/978-3-030-34732-1_4
M3 - Chapter
AN - SCOPUS:85101151117
SN - 9783030347314
T3 - SpringerBriefs in Mathematics
SP - 31
EP - 39
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 -