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Published in:
2020 | OriginalPaper | Chapter
8. Weak Convergence in \(L_\infty (X, \mathcal L, \lambda )\)
Author : John Toland
Published in: The Dual of L∞(X,L,λ), Finitely Additive Measures and Weak Convergence
Publisher: Springer International Publishing
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Abstract
This chapter opens by observing the relation between Dirac measures acting on C(\(\mathfrak G\),\(\tau \)) and elements of \(\mathfrak G\) acting on \(L_\infty \). This leads to a pointwise characterisation of weakly convergent sequences in \(L_\infty \) that settles some quite subtle questions about the weak convergence of specific sequences that are pointwise convergent.