TY - CHAP
T1 - Reconciling Representations
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 fact that in a general setting are isometrically isomorphic even though the dual of is represented by finitely additive measures, while the dual of C is represented by countably additive measures. Then, in the special case when X is a locally compact Hausdorff topological space, bounded linear functionals which on are represented by finitely additive measures are represented by countably additive measures when restricted to continuous functions. The relation between these two measures is explored in detail.
AB - This chapter deals with the fact that in a general setting are isometrically isomorphic even though the dual of is represented by finitely additive measures, while the dual of C is represented by countably additive measures. Then, in the special case when X is a locally compact Hausdorff topological space, bounded linear functionals which on are represented by finitely additive measures are represented by countably additive measures when restricted to continuous functions. The relation between these two measures is explored in detail.
UR - http://www.scopus.com/inward/record.url?scp=85101145369&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-34732-1_10
DO - 10.1007/978-3-030-34732-1_10
M3 - Chapter or section
AN - SCOPUS:85101145369
SN - 9783030347314
T3 - SpringerBriefs in Mathematics
SP - 87
EP - 93
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 -