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.
|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.|
|Number of pages||9|
|Publication status||E-pub ahead of print - 3 Jan 2020|
|Name||SpringerBriefs in Mathematics|
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